QuestionA truck drives at $60 \mathrm{mph}$ . A car enters 9 minutes later at $70 \mathrm{mph}$ . How long until the car passes the truck?

Studdy Solution

STEP 1

Assumptions1. The truck is driving at a constant speed of60 mph. The car is driving at a constant speed of70 mph3. The car enters the highway9 minutes after the truck4. We are asked to find the time it takes for the car to pass the truck, starting from the moment the car enters the highway

STEP 2

First, we need to find out how far the truck has traveled when the car enters the highway. We can do this by multiplying the truck's speed by the time it has been driving before the car enters the highway.
$Distance_{truck} = Speed_{truck} \\times Time_{truck}$

STEP 3

Now, plug in the given values for the truck's speed and the time it has been driving before the car enters the highway.
$Distance_{truck} =60 \, mph \\times9 \, minutes$

STEP 4

Since the speed is given in miles per hour and the time in minutes, we need to convert the time from minutes to hours.
$9 \, minutes = \frac{9}{60} \, hours$ $Distance_{truck} =60 \, mph \\times \frac{9}{60} \, hours$

STEP 5

Calculate the distance the truck has traveled.
$Distance_{truck} =60 \, mph \\times \frac{9}{60} \, hours =9 \, miles$

STEP 6

Now, we need to find out how long it takes for the car to travel the same distance plus the additional distance it needs to pass the truck. The additional distance is the difference in speeds between the car and the truck. The time can be found by dividing the distance by the car's speed.
$Time_{car} = \frac{Distance_{truck}}{Speed_{car}}$

STEP 7

Plug in the values for the truck's distance and the car's speed.
$Time_{car} = \frac{9 \, miles}{70 \, mph}$

STEP 8

Calculate the time it takes for the car to pass the truck.
$Time_{car} = \frac{ \, miles}{70 \, mph} =0.12857 \, hours$

STEP 9

Since the time is in hours and we need the answer in minutes, convert the time from hours to minutes.
$.12857 \, hours =.12857 \\times60 \, minutes$

STEP 10

Calculate the time in minutes and round to the nearest minute.
$Time_{car} =0.12857 \\times60 \, minutes =8 \, minutes$ From the time the car enters the highway, it will take8 minutes for the car to pass the truck.

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