Question

A boat takes 1.6 hours longer to go 36 kms up a river than down the river. If the speed of the water current is 4 km per hr, what is the speed of the boat in still water?

Answer 1

Let the speed of the boat in still water be “x”

Time taken to go for up of a river = `36/(x + 4)`

By the given condition

`36/(x - 4) - 36/(x + 4)` = 1.6

`(36(x + 4) - 36(x - 4))/((x + 4)(x - 4)) = 16/10`

`(36[x + 4 - (x - 4)])/(x^2 - 16) = 16/10`

`(36 xx 8)/(x^2 - 16) = 16/10`

16(x² – 16) = 36 × 8 × 10

x² – 16 = `(36 xx 8 xx 10)/16`

x² – 16 = 180

x² = 180 + 16

x² = 196

x² = `sqrt(196)`

= ± 14

The speed of the boat in still water = `(14"km")/"hr"`