Question

A car travels first half distance between two places at a uniform speed of 60 km/ hr. What should be it's uniform speed for the second half of the distance so that it's average speed over the entire journey becomes 90 km/hr?

Answer 1

total distance=2x

time for first half=x/60

time for second half=x/y

average speed= 2x/(x/60)+(x/y)

90=2x/(xy+60x/60y)

transposing,

3xy+180x=4xy

xy=180x

y=180km/hr.

therefore he has to travel at 180km/hr for the next half

Answer 2

Answer: The correct answer is 180 km/h.

Explanation:

It is given in the problem that a car travels first half distance between two places at a uniform speed of 60 km/ hr.

The expression for the average speed is as follows;

$A.V = \frac{Total distance}{Total time}$

Let the total distance covered be 2x.

time for first half=$\frac{x}{60}$

Let the speed during second half be y.

time for second half=$\frac{x}{y}$

Average speed= $\frac{2x}{\frac{x}{60}+\frac{x}{y}}$

Put Average speed= 90 km/h.

90= $\frac{2x}{\frac{x}{60}+\frac{x}{y}}$

Rearrange the above expression.

3xy+180x=4xy

xy=180x

y=180km/hr.

Therefore, a car travels at 180 km/hr for the second half.