Question

Jonas jogged up the hill at an average rate of of a 1/12 mile per minute and then walked down the hill at an average rate of of a 1/16 mile per minute. The round trip took him 42 minutes. What is the missing value in the table that represents the distance of the trip down the hill?
Table
Rate Time Distance
Up the Hill 1/12 x 1/12(x)
Down the Hill 1/16 42-x ?

Answer 1

Refer to attached table

Answer - $\frac{1}{16} (42-x)$ (In miles)

EXPLANATION

We know that distance traveled is calculated by multiplying average speed by total time.

According to the table,
Uphill average speed = $\frac{1}{12}$ (in miles per minute)
Uphill travel time = x (in minutes)
Total distance uphill = $\frac{1}{12} x$ (In miles)

The same way,
Downhill average speed = $\frac{1}{16}$ (in miles per minute)
Downhill travel time = 42 - x
Total distance downhill = Speed * Time = $\frac{1}{16} (42-x)$ (In miles)

Answer 2

The answer is (42-x) / 16

The formula for distance is d = rt; Where r = rate; t = time
d =? ; r = 1/16; t = 42-x
d = rt
   = 1/16 * 42-x
   = (42-x) / 16