Helps solving rate problem

Problem: Ramona cycles from her house to school at 15 miles per hour. Upon arriving, she realizes that it is Saturday and immediately cycles at 25 miles per hour. If the entire round-trip takes her 32 minutes, then what is her average speed, in miles per hour, for the entire round-trip?

I set up a table:

Leg 1: R: 15 D: x

Leg 2:: R: 25 D: x

Total: D: 2x T: 32 minutes

I know that average speed = total distance/total time... I have total time, so I need total distance (2x). I'm not too sure what to do from here. I did x/15 + x/25 = 32 minutes.. (That didn't go anywhere). Thanks for the help.

Re: Helps solving rate problem

r x t = d

going ... 15t = d

returning ... 25[(32/60) - t) = d

avg. speed = (total distance)/(total time) = (2d)/(32/60)

Re: Helps solving rate problem

Re: Helps solving rate problem

Hello, benny92000!

Quote:

Ramona cycles from her house to school at 15 mph. .Upon arriving, she realizes

that it is Saturday and immediately cycles home at 25 mph. .If the entire trip

takes her 32 minutes, what is her average speed for the entire trip?

Let $\displaystyle D$ = distance from home to school (in miles).

She went $\displaystyle D$ miles at 15 mph.

. . This took $\displaystyle \tfrac{D}{15}$ hours.

She went $\displaystyle D$ miles at 25 mph.

. . This took $\displaystyle \tfrac{D}{25}$ hours.

Her total time is 32 minutes $\displaystyle \left(\tfrac{8}{15}\text{ of an hour}\right)$

We have: .$\displaystyle \frac{D}{15} + \frac{D}{25} \:=\:\frac{8}{15} \quad\Rightarrow\quad D \,=\,5\text{ miles.}$

She went $\displaystyle 10$ miles in $\displaystyle \tfrac{8}{15}$ hours.

Her average speed was: .$\displaystyle \dfrac{10}{\frac{8}{15}} \:=\:\frac{75}{4} \:=\:18\tfrac{3}{4}\text{ mph.}$

Re: Helps solving rate problem

Quote:

Originally Posted by

**benny92000** Problem: Ramona cycles from her house to school at 15 miles per hour. Upon arriving, she realizes that it is Saturday and immediately cycles at 25 miles per hour. If the entire round-trip takes her 32 minutes, then what is her average speed, in miles per hour, for the entire round-trip?

I set up a table:

Leg 1: R: 15 D: x

Leg 2:: R: 25 D: x

Total: D: 2x T: 32 minutes

I know that average speed = total distance/total time... I have total time, so I need total distance (2x). I'm not too sure what to do from here. I did x/15 + x/25 = 32 minutes.. (That didn't go anywhere). Thanks for the help.

Hi benny92000,

Your equation d/15 +d/25 = total time was correct but you needed to change minutes to hours to get d=5miles