Question

from a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 14 miles per hour. in how many hours will they be 120 miles apart?

Answer 1

The two boats will be 120 miles apart in 5 hours.

Let x= distance travelled by boat 1 at 10 miles per hour.

Let y= distance travelled by boat y at 14 miles per hour.

Given, total distance travelled by both the boats=120 miles.

Thus, x+y=120------(i)

Let t denote the time factor,

then, Boat 1 travels x miles in T hours.

Boat 2 travels y miles in T hours.

We know, Distance= Rate * Time

Thus,  we can say, x= 10*T---------------(ii)

                               y=14*T-----------------(iii)

Adding equations ii and iii, we get

x+y=24T----------------(iv)

Now, subtract equation iv from i, we get

0=24T-120

120= 24T

thus, t=5

Hence, they will be 120 miles apart in 5 hours.

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