Question

The distance between two cities is 145 miles. A truck can cover this distance in 2. 5 hours. A car is 1. 5 times as fast as the truck. How long does it take them to meet, if they start moving towards each other simultaneously?.

Answer 1

The relative speed of the car to the truck while moving towards each other is the sum of the speed of both vehicles.

• The time it takes them to meet is 1 hour

Reasons:

The distance between the cities, d = 145 miles

The time it takes a truck to cover the distance = 2.5 hours

The speed of the car = 1.5 × Th speed of the truck

Required:

The time it takes them to meet if they are moving towards each other.

Solution:

• $\displaystyle Speed = \mathbf{ \frac{Distance}{Time}}$

$\displaystyle Speed \ of \ the \ truck, \ v_{truck} = \frac{145 \ miles}{2.5 \ hours} = \mathbf{58 \ mph}$

Therefore;

The speed of the car, $v_{car}$ = 1.5 × 58 mph = 87 mph

At the time, t, the truck and the car meet, we have;

$\mathbf{v_{car} \times t + v_{truck} \times t = d}$

Which gives;

87 × t + 58 × t = 145

$\displaystyle t = \mathbf{\frac{145}{87 + 58}} = 1$

• The time it takes them to meet, t = 1 hour

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