"It takes a boat 2 hours to travel downstream 28 miles and 2 hours to travel upstream 24 miles...

Question

 

What is the speed to the boat in still water in mph?

 

What is the speed of the current in mph?"

 

Hello, I'm not sure how to approach this problem. Can anyone help me?

Answer 1

time (t) = distance (d) / speed (s)

 

equation 1 - traveling downstream with the current

t1 = 2 hours = 28 miles / [boat speed (Sb) + current speed (Sc)]

2 = 28 / (Sb+Sc)

Sb+Sc = 14

 

equation 2 - traveling upstream against the current

t2 = 2 hours = 24 miles / [boat speed (Sb) - current speed (Sc)]
2 = 24 / (Sb-Sc)

Sb-Sc = 12

 

solve two equations in two unknowns by adding the two equations

2Sb = 26

Sb (boat speed in still water) = 13 miles per hour (mph)

substitute in equation 1, then

13 + Sc = 14

Sc (current speed) = 1 miles per hour (mph)