QuestionA truck driver goes 60 mph to deliver and 45 mph back, taking 7 hours total. Find the time difference between trips.

Studdy Solution

STEP 1

Assumptions1. The truck driver averages60 miles per hour on the delivery trip. . The truck driver averages45 miles per hour on the return trip.
3. The total driving time for both trips is7 hours.

STEP 2

Let's denote the distance of the trip as $d$ , the time spent on the delivery trip as $t1$ , and the time spent on the return trip as $t2$ .

STEP 3

We know that speed is equal to distance divided by time, so we can write the following equations for the delivery trip and the return trip $d =60t1$ $d =45t2$

STEP 4

Since the distance of the delivery trip and the return trip is the same, we can equate the two equations $60t1 =45t2$

STEP 5

To isolate $t2$ , divide both sides of the equation by45 $t2 = \frac{60t1}{45}$

STEP 6

implify the equation $t2 = \frac{4}{3}t1$

STEP 7

We know that the total driving time is7 hours, so we can write the following equation $t1 + t2 =7$

STEP 8

Substitute $t2$ from the previous step into this equation $t1 + \frac{4}{3}t1 =7$

STEP 9

Combine like terms $\frac{7}{3}t =7$

STEP 10

To solve for $t$ , divide both sides of the equation by $\frac{7}{3}$ , which is equivalent to multiplying by $\frac{3}{7}$ $t =7 \times \frac{3}{7}$

STEP 11

implify the equation to find the value of $t$ $t =3$

STEP 12

Substitute $t =$ into the equation $t2 = \frac{4}{}t$ to find the value of $t2$ $t2 = \frac{4}{} \times$

STEP 13

implify the equation to find the value of $t2$ $t2 =$

STEP 14

To find out how much longer the return trip takes than the delivery, subtract the time of the delivery trip from the time of the return trip $\Delta t = t2 - t$

STEP 15

Substitute the values of $t2$ and $t$ into the equation $\Delta t =4 -3$

STEP 16

Calculate the difference $\Delta t =$ The return trip takes hour longer than the delivery.

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QuestionA truck driver goes 60 mph to deliver and 45 mph back, taking 7 hours total. Find the time difference between trips.

Studdy Solution

STEP 1

Assumptions1. The truck driver averages60 miles per hour on the delivery trip. . The truck driver averages45 miles per hour on the return trip.
3. The total driving time for both trips is7 hours.

STEP 2

Let's denote the distance of the trip as $d$ , the time spent on the delivery trip as $t1$ , and the time spent on the return trip as $t2$ .

STEP 3

We know that speed is equal to distance divided by time, so we can write the following equations for the delivery trip and the return trip $d =60t1$ $d =45t2$

STEP 4

Since the distance of the delivery trip and the return trip is the same, we can equate the two equations $60t1 =45t2$

STEP 5

To isolate $t2$ , divide both sides of the equation by45 $t2 = \frac{60t1}{45}$

STEP 6

implify the equation $t2 = \frac{4}{3}t1$

STEP 7

We know that the total driving time is7 hours, so we can write the following equation $t1 + t2 =7$

STEP 8

Substitute $t2$ from the previous step into this equation $t1 + \frac{4}{3}t1 =7$

STEP 9

Combine like terms $\frac{7}{3}t =7$

STEP 10

To solve for $t$ , divide both sides of the equation by $\frac{7}{3}$ , which is equivalent to multiplying by $\frac{3}{7}$ $t =7 \times \frac{3}{7}$

STEP 11

implify the equation to find the value of $t$ $t =3$

STEP 12

Substitute $t =$ into the equation $t2 = \frac{4}{}t$ to find the value of $t2$ $t2 = \frac{4}{} \times$

STEP 13

implify the equation to find the value of $t2$ $t2 =$

STEP 14

To find out how much longer the return trip takes than the delivery, subtract the time of the delivery trip from the time of the return trip $\Delta t = t2 - t$

STEP 15

Substitute the values of $t2$ and $t$ into the equation $\Delta t =4 -3$

STEP 16

Calculate the difference $\Delta t =$ The return trip takes hour longer than the delivery.

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QuestionA truck driver goes 60 mph to deliver and 45 mph back, taking 7 hours total. Find the time difference between trips.

Studdy Solution

STEP 1

Assumptions1. The truck driver averages60 miles per hour on the delivery trip. . The truck driver averages45 miles per hour on the return trip.3. The total driving time for both trips is7 hours.

STEP 2

Let's denote the distance of the trip as ddd, the time spent on the delivery trip as t1t1t1, and the time spent on the return trip as t2t2t2.

STEP 3

We know that speed is equal to distance divided by time, so we can write the following equations for the delivery trip and the return tripd=60t1d =60t1d=60t1d=45t2d =45t2d=45t2

STEP 4

Since the distance of the delivery trip and the return trip is the same, we can equate the two equations60t1=45t260t1 =45t260t1=45t2

STEP 5

To isolate t2t2t2, divide both sides of the equation by45t2=60t145t2 = \frac{60t1}{45}t2=4560t1​

STEP 6

implify the equationt2=43t1t2 = \frac{4}{3}t1t2=34​t1

STEP 7

We know that the total driving time is7 hours, so we can write the following equationt1+t2=7t1 + t2 =7t1+t2=7

STEP 8

Substitute t2t2t2 from the previous step into this equationt1+43t1=7t1 + \frac{4}{3}t1 =7t1+34​t1=7

STEP 9

Combine like terms73t=7\frac{7}{3}t =737​t=7

STEP 10

To solve for ttt, divide both sides of the equation by 73\frac{7}{3}37​, which is equivalent to multiplying by 37\frac{3}{7}73​t=7×37t =7 \times \frac{3}{7}t=7×73​

STEP 11

implify the equation to find the value of tttt=3t =3t=3

STEP 12

Substitute t=t =t= into the equation t2=4tt2 = \frac{4}{}tt2=4​t to find the value of t2t2t2t2=4×t2 = \frac{4}{} \timest2=4​×

STEP 13

implify the equation to find the value of t2t2t2t2=t2 =t2=

STEP 14

To find out how much longer the return trip takes than the delivery, subtract the time of the delivery trip from the time of the return tripΔt=t2−t\Delta t = t2 - tΔt=t2−t

STEP 15

Substitute the values of t2t2t2 and ttt into the equationΔt=4−3\Delta t =4 -3Δt=4−3

STEP 16

Calculate the differenceΔt=\Delta t =Δt=The return trip takes hour longer than the delivery.

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Assumptions1. The truck driver averages60 miles per hour on the delivery trip. . The truck driver averages45 miles per hour on the return trip.
3. The total driving time for both trips is7 hours.

Let's denote the distance of the trip as $d$ , the time spent on the delivery trip as $t1$ , and the time spent on the return trip as $t2$ .

We know that speed is equal to distance divided by time, so we can write the following equations for the delivery trip and the return trip $d =60t1$ $d =45t2$

Since the distance of the delivery trip and the return trip is the same, we can equate the two equations $60t1 =45t2$

To isolate $t2$ , divide both sides of the equation by45 $t2 = \frac{60t1}{45}$

implify the equation $t2 = \frac{4}{3}t1$

We know that the total driving time is7 hours, so we can write the following equation $t1 + t2 =7$

Substitute $t2$ from the previous step into this equation $t1 + \frac{4}{3}t1 =7$

Combine like terms $\frac{7}{3}t =7$

To solve for $t$ , divide both sides of the equation by $\frac{7}{3}$ , which is equivalent to multiplying by $\frac{3}{7}$ $t =7 \times \frac{3}{7}$

implify the equation to find the value of $t$ $t =3$

Substitute $t =$ into the equation $t2 = \frac{4}{}t$ to find the value of $t2$ $t2 = \frac{4}{} \times$

implify the equation to find the value of $t2$ $t2 =$

To find out how much longer the return trip takes than the delivery, subtract the time of the delivery trip from the time of the return trip $\Delta t = t2 - t$

Substitute the values of $t2$ and $t$ into the equation $\Delta t =4 -3$

Calculate the difference $\Delta t =$ The return trip takes hour longer than the delivery.