Math Problem of the Week - Algebra and Up - Mar. 20, 2022 to Mar. 26, 2022

Algebra and Up: 

Question: The speed of Arman's new boat in still water is 30 mph. It takes him 6 hours to go to his friend's house upstream from his boat dock and only 4 hours to come back to his dock going downstream. How fast is the current?

Answer: 6 mph

Solution: 

We can use the formula, d = rt. Arman traveled the same distance upstream and downstream so we can set the distance upstream equal to the distance downstream. Letting x = speed of the current, the rate is the speed of the boat ± the speed of the current.

upstream: d = (30 − x)6

downstream: d = (30 + x)4

(30 − x)6 = (30 + x)4

180 − 6x = 120 + 4x

x = 6 mph