hard math question

[cockermongol]

I found this on an SAT Practice Test. Have fun!

A train running between two towns arrives at its destination 10 minutes late when it goes 40 miles per hour and 16 minutes late when it goes 30 miles per hour. What is the distance between the towns?

I had a lot of trouble with this question...

[CoolHand]

I found this on an SAT Practice Test. Have fun!

A train running between two towns arrives at its destination 10 minutes late when it goes 40 miles per hour and 16 minutes late when it goes 30 miles per hour. What is the distance between the towns?

I had a lot of trouble with this question...

I'm pretty sure the answer is 12 miles, but I've been full of crap before, so I may be wrong.

Since its a constant velocity kinda thing, you can just use D=V*T (right? )

You can set up the simultanius equations using the differences in time and velocity, and solve for T and D.

Meaning that if it takes 6 mins longer, going 10 mph slower, the towns are 12 miles apart. (unless I've made a computational error somewhere, which is entirely possible)

Do you happen to have the correct answer?

[spantol]

Nothing like Algebra at 2:30am.

Coolhand's got it. Here's the process:

d = rt.

At 40mph, d = (2/3)*(x+10)
At 30mph, d = (1/2)*(x+16)

Set the two equal to each other, and solve for x:

2/3x + 6.67 = x/2 + 8

x = 8

Stick x back in to the original equations, and solve for d:

d = (2/3)*(8+10)
d = (1/2)*(8+16)

d = 12