Question

A motorboat left a harbor and traveled to an island at an average rate of 13 knots. The average speed on the return trip was 10 knots. If the total trip took 6.9 hours, how far is the harbor from the island?

Answer 1

The distance between harbor & the island D = 72.12 km

Explanation:

Let the total distance between harbor & island = D

Motor boat going to the island at speed
`S_(1)` = 13 knots = 24
`(km)/(hr)`

Return speed of the motorboat
`S_(2)` = 10 knots = 18.52
`(km)/(hr)`

The total time taken for both journey = 6.9 hours

`(D)/(S_(1) ) + (D)/(S_(2) ) = 6.9`

`(D)/(24) + (D)/(18.52) = 6.9`

`D ((1)/(24) + (1)/(18.52) ) = 6.9`

D ( 0.0956 ) = 6.9

⇒ D = 72.12 km

This is the distance between harbor & the island.