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Math  /  Numbers & Operations

QuestionThe Eefmont race track known es "Big Sandy" is 14, miles long. In 1973, Secretariat won the Belmont Stakes race in 2 minutes and 30 seconds. Assuming lie ran on "Big Sandy", what wets tha unit sposan? (C) 10 mph (1) 40 mph
036 mph (3) 38 mph

Studdy Solution

STEP 1

What is this asking? How fast was Secretariat running on average during his Belmont Stakes win? Watch out! The time is given in minutes *and* seconds, so we need to be careful with units!

STEP 2

1. Convert time to hours
2. Calculate speed

STEP 3

Alright, let's **tackle this time conversion**!
We're given **2 minutes and 30 seconds**.
We need to get this all in terms of hours.

STEP 4

First, let's **convert the minutes to hours**.
There are 6060 minutes in an hour, so we divide our **2 minutes** by 6060: 2 minutes60minuteshour=260 hours=130 hours. \frac{2 \text{ minutes}}{60 \frac{\text{minutes}}{\text{hour}}} = \frac{2}{60} \text{ hours} = \frac{1}{30} \text{ hours}. So, **2 minutes** is equal to 130\frac{1}{30} of an hour.

STEP 5

Next, let's **convert the seconds to hours**.
There are 6060 seconds in a minute and 6060 minutes in an hour, so there are 60⋅60=360060 \cdot 60 = 3600 seconds in an hour.
We divide our **30 seconds** by 36003600: 30 seconds3600secondshour=303600 hours=1120 hours. \frac{30 \text{ seconds}}{3600 \frac{\text{seconds}}{\text{hour}}} = \frac{30}{3600} \text{ hours} = \frac{1}{120} \text{ hours}. So, **30 seconds** is equal to 1120\frac{1}{120} of an hour.

STEP 6

Now, let's **add these two time amounts together** to get the **total time in hours**: 130 hours+1120 hours=4120 hours+1120 hours=4+1120 hours=5120 hours=124 hours. \frac{1}{30} \text{ hours} + \frac{1}{120} \text{ hours} = \frac{4}{120} \text{ hours} + \frac{1}{120} \text{ hours} = \frac{4+1}{120} \text{ hours} = \frac{5}{120} \text{ hours} = \frac{1}{24} \text{ hours}. Great! The **total time** is 124\frac{1}{24} of an hour.

STEP 7

Remember, **speed is distance divided by time**.
We're given that the **distance** is 1141\frac{1}{4} miles, which is the same as 54\frac{5}{4} miles.
We just calculated the **time** to be 124\frac{1}{24} hours.

STEP 8

Let's **plug these values into our speed formula**: Speed=DistanceTime=54 miles124 hours=54⋅241mileshour=5⋅244⋅1mileshour=1204mileshour=30mileshour. \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{5}{4} \text{ miles}}{\frac{1}{24} \text{ hours}} = \frac{5}{4} \cdot \frac{24}{1} \frac{\text{miles}}{\text{hour}} = \frac{5 \cdot 24}{4 \cdot 1} \frac{\text{miles}}{\text{hour}} = \frac{120}{4} \frac{\text{miles}}{\text{hour}} = 30 \frac{\text{miles}}{\text{hour}}.

STEP 9

Secretariat's unit speed was 3030 mph.

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