# Math Help - Distance and Speed related word problem

1. ## Distance and Speed related word problem

Hey there. I have a word problem here, I think this is the right place to post. I am trying to get back into understanding algebra but I ran into a word problem that I can not begin to think of a formula able to solve that D=R*T can't. I guess I need help understanding how to formulate the problem;

A freight train left Washington traveling
east 7.8 hours before a diesel train. The
diesel train traveled in the opposite direction
going 17.1 mph slower then the freight train
for ten hours after which time the trains
were 941 mi. apart. How fast did the freight
train travel?

Your attention is greatly appreciated. Thank you!

2. ## Re: Distance and Speed related word problem

You can use D = rt here.

For example, suppose the freight train traveled at r mph for 17.8 hours (because it traveled for 7.8 hrs, then another 10 hrs). Then the diesel train traveled at r - 17.1 mph for 10 hours. We can add their distances because the trains are in the opposite direction:

$17.8r + 10(r - 17.1) = 941$

Solve for r.

3. ## Re: Distance and Speed related word problem

Thank you very much! It makes a lot more sense now.

4. ## Re: Distance and Speed related word problem

Originally Posted by richard1234
You can use D = rt here.
For example, suppose the freight train traveled at r mph for 17.8 hours (because it traveled for 7.8 hrs, then another 10 hrs). Then the diesel train traveled at r - 17.1 mph for 10 hours. We can add their distances because the trains are in the opposite direction:
$17.8r + 10(r - 17.1) = 941$
Solve for r.
Disagree; 941 is not the distance travelled: it is distance that the 2 trains are apart...
(or did I miss something?):

F(@f mph)-------------->[17.8 h].....(941 miles).....[10 h]<-------(@f-17.1 mph)D

Let freight train speed = f and total distance between the 2 starting points = x

x - 17.8f - 10(f - 17.1) = 941 ; simplifies to x = 27.8f + 770 [1]

You can now use any speed for f (greater than 17.1); say 100, then:
[1] x = 27.8(100) + 770 = 3550 miles.

Diesel's speed will be 100 - 17.1 = 82.9
Distance = 82.9(10) = 829

1780 + 829 + 941 = 3550

5. ## Re: Distance and Speed related word problem

Yes, it is possible to interpret the problem in such a way that cannot solve it! It is also possible to interpret in such a way that we can and that makes much more sense. We are told that "A freight train left Washington" going east and that later a diesel left in the opposite direction. Although it is not said explicitely that language certainly implies that the diesel also left from Washington. It simply makes no sense to assume that the diesel left from some competely undisclosed location.

6. ## Re: Distance and Speed related word problem

Re-read original...agree with you; guess I'm too used to these being 2 "things" starting from different locations...

7. ## Re: Distance and Speed related word problem

I worked out richard1234's equation and it works out to r=40.32~ mph. The answer key states it is just 40 mph. I'm wondering if the 40.32 answer is correct but just asks to round off (40).

Thank you guys for giving your deliberations.

8. ## Re: Distance and Speed related word problem

You should get exactly 40 mph right off the bat.
f - freight train speed

f(10 + 7.8) + 10(f - 17.1) = 941
10f + 7.8f + 10f - 171 = 941
27.8f = 1112
f = 40

9. ## Re: Distance and Speed related word problem

Yeah, I got exactly 40.