QuestionA car and a motorcycle start from the same point and travel in opposite directions.
Given that the car travels at $50 \mathrm{~km} / \mathrm{h}$ , while the motorcycle travels at $40 \mathrm{~km} / \mathrm{h}$ , after how many hours will they be 315 km apart?

Studdy Solution

STEP 1

1. The car and motorcycle start from the same point.
2. They travel in opposite directions.
3. The car travels at a speed of $50 \, \text{km/h}$ .
4. The motorcycle travels at a speed of $40 \, \text{km/h}$ .
5. We need to find the time it takes for them to be $315 \, \text{km}$ apart.

STEP 2

1. Define a variable for time.
2. Write an equation that models the total distance.
3. Solve the equation for time.

STEP 3

Define a variable for time. Let $t$ represent the time in hours after which they are $315 \, \text{km}$ apart.

STEP 4

Write an equation that models the total distance. Since they are traveling in opposite directions, the total distance between them after $t$ hours is the sum of the distances each has traveled:
$50t + 40t = 315$

STEP 5

Solve the equation for time. Combine like terms:
$90t = 315$
Divide both sides by $90$ to isolate $t$ :
$t = \frac{315}{90}$
Simplify the fraction:
$t = \frac{7}{2}$
$t = 3.5$
The time after which they will be $315 \, \text{km}$ apart is:
$\boxed{3.5}$ hours

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