# Helps solving rate problem

• Nov 21st 2011, 02:22 PM
benny92000
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.
• Nov 21st 2011, 02:33 PM
skeeter
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)
• Nov 21st 2011, 02:55 PM
benny92000
Re: Helps solving rate problem
I got 18.75. Thanks!
• Nov 21st 2011, 03:42 PM
Soroban
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 $D$ = distance from home to school (in miles).

She went $D$ miles at 15 mph.
. . This took $\tfrac{D}{15}$ hours.

She went $D$ miles at 25 mph.
. . This took $\tfrac{D}{25}$ hours.

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

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

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

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

• Nov 21st 2011, 04:27 PM
bjhopper
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