Question

A man moves from A to B at the rate of 4km an hour. had he moved at the rate of 11/3 km an hour , he would have taken 3 hours more to move that distance . find the distance A and B.

Answer 1

Given,

A man moves from A to B at the rate of 4km/hr.

And, If he had moved at the rate of 11/3 km/hr he would have taken 3 hours more to cover the same distance.

In Case 1 :-

Let the distance travelled be, d,

Time taken be t .

So,

⇒ Distance = Speed × Time

⇒ d = 4 × t

⇒ d = 4t km ...(1)

In Case 2 :-

Also, If he had moved at the rate of 11/3 km/hr he would have taken 3 hours more.

So, Here

Time taken be, t + 3

Distance is still same i.e., d

⇒ Distance = Speed × Time

⇒ d = 11/3 ( t + 3 )

⇒ d = (11t / 3) + 11 ...(2)

Since, The man travelled the same distance

∴ (1) = (2) = d

⇒ 4t = 11t / 3 + 11

⇒ 4t = (11t + 33) / 3

⇒ 12t = 11t + 33

⇒ t = 33

Now, Substitute t = 33 in (1)

⇒ Distance = 4 × 33

⇒ Distance = 132 km

Hence, The distance between A and B is 132 km.

Answer 2

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