Algebra word problems

Question

Two trains leave towns 560 kilometers apart at the same time and travel toward each other. One train travels 16km/h slower than the other. If they meet in 2

hours, what is the rate of each train?

Answer 1

I like to make a table when I do this type of problem:

And I also note UNITS and recall the formula: Distance = Rate X Time

Assume Train #2 is the slower Train. We are told that Train2 is 16 mph slower than Train1

DIST ( m) RATE(mph) TIME(hrs)

Train#1 | D1 R1 2

Train#2 | D2 ( R1 - 16 ) 2

Because we know that the total distance is 560, we can add D1 and D2

560 = D1 + D2 = R1*2 + (R1-16)*2

560 = R1*2 *R1*2 -16*2 = R1*4 -32

solve for R1*4 = 560+32 = 592 or R1 = 148.

solve for R2 using R2 = R1-16 = 148 -16 = 132.

CHECK: train1 travels 148*2 miles = 296 miles

train2 travels 132^2 = N 264 miles

total distance is 296 + 264 = 560 miles

Answer 2

2r + 2(r - 16) = 550

Can you solve for r and answer?