If a person walks 20 km/h slower than his usual speed, he takes 4 hours more to cover a certain distance. If he walks 40 km/hr faster than his usual s

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answered Feb 27, 2022 by tushark (113k points)
selected Feb 27, 2022 by Pravask

Best answer

Correct Answer - Option 4 : 960

Given:

A person walks 20 km/h slower than his usual speed, he takes 4 hours more to cover a certain distance

He walks 40 km/hr faster than his usual speed, he takes 4 hours less to cover that distance.

Formula used:

Time = Distance/Speed

Speed = Distance/Time

Calculation:

Let the original speed be m km/h and the distance is x km

For the first case get,

x/(m - 20) - x/m = 4

⇒ x[(m - m + 20)]/m(m - 20) = 4

⇒ x = m(m - 20)/5 ----(1)

Again from the 2nd case get,

x/m - x/(m + 40) = 4

⇒ x(m + 40 - m)/m(m + 40) = 4

⇒ 40x/m(m + 40) = 4

⇒ x = m(m + 40)/10 ----(2)

From (1) and (2) get,

m(m - 20)/5 = m(m + 40)/10

⇒ 5m + 200m = 10m - 200

⇒ -5m = -400

⇒ m = 80

Original speed = 80 km/hr

Now, from equation(1),

x/(m - 20) - x/m = 4

⇒ x/(80 - 20) - x/80 = 4

⇒ x/60 - x/80 = 4

⇒ (4x - 3x)/240 = 4

⇒ x/240 = 4

⇒ x = 960

∴ The distance (in km) is 960.

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