Trouble finding d.

J

JohnnyGrey

New member
Joined
Jul 21, 2008
Messages
4
Here us the problem:

Johnny walks to school at 3 miles an hour, and runs home at 5 mph. The round trip takes 1 hour. What is the distance (round trip)?

The choices given are a) 3 b) 3.12 c) 3.75 d)4 e)5

Since the distance to the school is the same as the distance back, I figured I would have to do something with 1/2d for each fo the speeds, but I am unable to come up with any of the numbers given in the choices.

This is the approach I took:

d = t/s
t = ds

(1/2d)(3) + (1/2d)(5) = 1 hour
I have also done this same equation using 60 minutes instead of 1 hour.

I can't figure out what I am doing wrong, or a different approach I should take. Does anyone know how to solve this?
 
Name things. Let d represent the distance to school. Let t[sub:1up4lfhm]g[/sub:1up4lfhm] represent time to go to school. Let t[sub:1up4lfhm]r[/sub:1up4lfhm] represent the time it takes him to return from school.
Going to school you have rate = 3 mi/hr and distance = d. Therefore, how can you represent the time (t[sub:1up4lfhm]g[/sub:1up4lfhm]) in terms of r and d? t=?
Returning from school you have r = 5 and distance still = d. How can you represent the time t[sub:1up4lfhm]r[/sub:1up4lfhm] in terms of his rate and distance.
Once you have dicided that, you know that the time going and the time returning add up to one hour. Write your equation and solve for d.
 
This makes me feel a bit dumb saying this, but I'm still not quite understanding what to do :?
 
let d = one way distance to school
t = time going to school in hours
1-t = time going home in hours

(rate)(time) = distance

walking to school ...
3t = d

running home ...
5(1-t) = d

now ... what can you say about the expressions 3t and 5(1-t) ?

can you solve for t?

can you then determine the distance to school (d) and double it to answer the round trip question?
 
I'm doing the equations like this:

3t =d
5(1-t) = d

3t = 5(1-t)
3t = 5 - 5t
8t = 5
t = .62


3(.62) = 1.86
5 -5(.62) = 1.90

Am I doing something wrong for the numbers not to be coming out exactly equal? Also, 2d doesn't quite equal the numbers I was given as choices... do you think that's ok? Should rounding be expected? (It's from an SAT prep book).
 
5/8 = .625, not .62

t = .625 hr

3t = 1.875 miles ... double that, 3.75 miles
 
Aahhh... I see now. The calculator I used only went to the second decimal place...

Thank you so much!
 
JohnnyGrey said:
The calculator I used only went to the second decimal place...
Click to expand...

I think you need to read the calculator manual. All the calculators I know of - keeps track of 8 decimals - unless "commanded" to other places.
 
You must log in or register to reply here.
Top