Question

Two trains start from towns 128 miles apart and travel towards each other on parallel tracks. They pass each other 1.6 hours later. If one train travels 10 mph faster than the other, find the speed of each train.

Answer 1

Let s and t be the speeds of the two trains. What are the two equations you write down in terms of s and t?

One comes from: "Two trains start from towns 128 miles apart and travel towards each other on parallel tracks. They pass each other 1.6 hours later."

The other from: "If one train travels 10 mph faster than the other..."

Answer 2

For the first one, remember that
(Speed) = (Distance) / (Time)

Answer 3

so the first equation would be x = 128/1.6 ?

Answer 4

What's x here? we want equations in s and t, since these are the variables we want to solve for.

Answer 5

s + t = 128/1.6 ?

Answer 6

Exactly, and 128/1.6 = 80. Hence one equation is
s + t = 80.

Now, what's the other equation?

Answer 7

umm s + 10 = 80 ?

Answer 8

No. "one train travels 10 mph faster than the other" How do express that in terms of s and t? If you like, assume t is the faster speed.

Answer 9

t + 10 = s - 10 ?

Answer 10

No, that can't be right. If I'm driving a car at 50 mph and you're driving another one 10 mph faster, then it isn't that
60 + 10 = 50 - 10

It's that 50 + 10 = 60.

So t = s + 10

Answer 11

so the two equations are s+t = 80 and t =s+10 ?

Answer 12

Yes. Now solve.

Answer 13

how? o.o

Answer 14

You have two equations, two unknowns.
s + t = 80
t = s + 10.

I would substitute the second equation into the first one to eliminate t. Then you will have an equation in s. Solve for s. Then substitute back into the second equation to solve for t.

Answer 15

what do you mean by "substitute the second equation into the first?

Answer 16

This is the method of solving simultaneous equations. I'm nervous that you don't recognize it. You cannot solve this problem without knowing how to solve simultaneous equations. Did you miss a few days of school or something?

Answer 17

i cant focus..