Question

Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

Answer 1

Answer:

She jogged uphill for 1.6 miles

Step-by-step explanation:

Given:

Uphill speed = 3 miles per hour

Downhill speed = 8 miles per hour

Total time to cover uphill and downhill = 40 minutes = $\frac{40}{60}$ hours

Average speed = 4 miles per hour

Now,

Let the distance of uphill be 'x'

and downhill distance be 'y'

Time = $\frac{\textup{Distance}}{\textup{Speed}}$

therefore,

$\frac{x}{3}+\frac{y}{8}=\frac{40}{60}$

or

$\frac{8x+3y}{3\times8}=\frac{2}{3}$

or

8x + 3y = 16  ...........(1)

also,

Average speed = $\frac{\textup{Total distance}}{\textup{Total time}}$

or

4 = $\frac{\textup{x+y}}{\frac{40}{60}}$

or

4 × 40 = 60(x + y)

or

3x + 3y = 8  

or

3y = 8 - 3x         ............(2)

substituting 2 in 1, we get

8x + (8 - 3x) = 16

or

5x + 8 = 16

or

5x = 8

or

x = 1.6 miles

and,

3y = 8 - 3x  

or

3y = 8 - 3(1.6)  

or

3y = 8 - 4.8

or

y = 1.067 miles

Hence,

She jogged uphill for 1.6 miles