How do you solve distance, rate, & time word problems (algebra 2)?

Question

Ex: a boat travels at a rate of 15 km per hour in still water. It travels 60 km upstream in the same time it travels 90 km downstream. What is the rate of the water?

Answer 1

Let x be the rate of the water

 

rate of boat upstream = 15 - x

 

rate of boat downstream = 15 + x

 

time = distance/rate

 

60/(15-x) = 90/(15+x)

 

60(15+x) = 90(15-x)   (cross multiplying)

 

2(15+x) = 3(15-x)  dividing through by 30

 

30 + 2x = 45 - 3x

 

5x = 15

 

x = rate of the water = 3 mph