Question8-Two automobiles are 150 kilometers apart and traveling toward each other. One automobile is moving at $60 \mathrm{~km} / \mathrm{h}$ and the other is moving at $40 \mathrm{~km} / \mathrm{h} \mathrm{mph}$ . In how many hours will they meet? A. 2.5 B. 2.0

Studdy Solution

STEP 1

1. Two automobiles are initially 150 kilometers apart.
2. One automobile travels at a speed of 60 km/h.
3. The other automobile travels at a speed of 40 km/h.
4. Both automobiles are moving toward each other.
5. We need to find the time in hours when they will meet.

STEP 2

1. Understand the concept of relative speed.
2. Calculate the relative speed of the two automobiles.
3. Use the formula for time to find when they will meet.

STEP 3

Understand the concept of relative speed. When two objects move toward each other, their relative speed is the sum of their individual speeds.

STEP 4

Calculate the relative speed of the two automobiles.
The speed of the first automobile is $60 \, \text{km/h}$ .
The speed of the second automobile is $40 \, \text{km/h}$ .
The relative speed is:
$60 \, \text{km/h} + 40 \, \text{km/h} = 100 \, \text{km/h}$

STEP 5

Use the formula for time to find when they will meet.
The formula to calculate time is:
$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
Substitute the known values:
$\text{Time} = \frac{150 \, \text{km}}{100 \, \text{km/h}}$
$\text{Time} = 1.5 \, \text{hours}$
The correct answer is not listed among the options provided, but the calculated time for the automobiles to meet is:
$\boxed{1.5}$

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