1.) Train A goes 12mph slower than Train B. Train A travels 230 miles in the same time that Train B travels 290 miles. Find the speed of each train.

2.) Zeno takes 3 hr longer to paint a floor than it takes Lia. When they work together, it takes them 2 hrs. How long would each take to do the job alone?

3.) A boat travels 15 km/h in still water. If the boat travels 140 km downstream in the same time it takes to travel 35 km upstream. What is the speed of the river?

I’m not sure what sort of equations to use in order to set up the problem..

Any help would be great, thanks :)

very simple

1) let speed of train A is Va, B be Vb

given, Va = Vb - 12………………eqn 1

speed= distance/time

time taken is same for each of the train, let it be t

given, distance traveled by A/ speed of A = distance traveled by B/speed of B…just equating time

or

230/Va = 290/Vb

put Vb= Va + 12 from equation 1 and solve 

2) Let time taken by Lia to paint a floor be x hours.

Thus, time taken by Zeno would be x + 3 hours.

This simply means when alone, in 1 hour,

Lia completes 1/x of the floor, while

Zeno completes 1/(x+3) of the floor.

If working together, in 1 hour,

Both will complete 1/x + 1/(x+3) of the floor

Since if working together, it takes them 2 hours to complete the job, in 1 hour they would complete 1/2 of the whole floor, or in other word:

1/x + 1/(x+3) = 1/2

[(x+3) + x] / [(x)(x+3)] = 1/2

(2x+3)/(x^2+3x) = 1/2

2(2x+3)=(x^2+3x)

4x+6=x^2+3x

x^2-x-6=0

Solving for x, x=3 hours or x=-2 (Not acceptable, as time taken to paint a floor can’t be negative)