QuestionA truck travels 50 miles per hour. A car leaves 30 minutes later and catches the truck at 8:00 A.M. Find the car's speed.

Studdy Solution

STEP 1

Assumptions1. The truck travels at a speed of50 miles per hour. . The truck starts its journey at600 A.M.
3. The car starts its journey half an hour later, at630 A.M.
4. The car catches up to the truck at800 A.M.
5. Both vehicles are traveling in the same direction.

STEP 2

First, we need to find out how long the truck has been traveling when the car catches up to it. This is from600 A.M. to800 A.M., which is2 hours.

STEP 3

Next, we calculate how far the truck has traveled in this time. We can do this by multiplying the speed of the truck by the time it has been traveling.
$Distance_{truck} = Speed_{truck} \\times Time_{truck}$

STEP 4

Now, plug in the given values for the speed of the truck and the time it has been traveling to calculate the distance.
$Distance_{truck} =50 \, miles/hour \\times2 \, hours$

STEP 5

Calculate the distance the truck has traveled.
$Distance_{truck} =50 \, miles/hour \\times2 \, hours =100 \, miles$

STEP 6

Now, we need to find out how long the car has been traveling when it catches up to the truck. This is from630 A.M. to800 A.M., which is1.5 hours.

STEP 7

Since the car catches up to the truck at the same distance where the truck is, the distance traveled by the car is also100 miles. Now, we can find the speed of the car by dividing the distance traveled by the time it has been traveling.
$Speed_{car} = Distance_{car} / Time_{car}$

STEP 8

Plug in the values for the distance traveled by the car and the time it has been traveling to calculate the speed.
$Speed_{car} =100 \, miles /1.5 \, hours$

STEP 9

Calculate the speed of the car.
$Speed_{car} =100 \, miles /.5 \, hours =66.7 \, miles/hour$ The speed of the car is approximately66.7 miles per hour.

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