Question

a boat can travel downstream 5 miles in 40min. and make the return trip upstream in 60 min. Show how to calculate the speed of the boat and the speed of the river. just show me the steps needed to do this problem.

Answer 1

let the speed of boat in still water be = x miles/hour
let the speed of river = y miles/hour

then speed of boat while going downstream = (x + y) miles/hour
and the speed of boat while going upstream = (x - y) miles/hour

travel downstream 5 miles in 40min. and make the return trip upstream in 60 min.

we know distance = speed * time

so when boat travels 5 miles downstream in 40 min
5 = (x + y) * 40 ==> 40x + 40y = 5 -----------------(1)

and when boat travels 5 miles upstream in 60 min
5 = (x - y) * 60 ==> 60x - 60y = 5 ------------------(2)

so now you hv a pair of linear equations in two variables x and y

if u know how to solve them then you can get values of x and y i.e. speed of boat and speed of river respectively....

if u need help, let me know...