1. ## Rates word problems

Just got three questions that I need help with but have little idea how to solve them.

2. Originally Posted by delicate_tears
Just got three questions that I need help with but have little idea how to solve them.

Let say the average speed was x

Time taken to travel this distance was = 108/x

But from the question

time taken with average speed (x+2)

= 108/(x+2)

But according to given condition

108/(x+2)= 108/x - 4.5

Solve for x

3. Originally Posted by delicate_tears
Just got three questions that I need help with but have little idea how to solve them.

Lets say that the speed of fast train =x

and that of slow one= x-20

Time taken by fast train to reach = 250/x

time taken by slow train to reach = 250/(x-20)

Its given that the difference between the starting time is 10minutes

and the total difference of time taken =3hours 30 mins

This gives that the slower train takes a time =250/x + 3hours 20mins

=250/x + 3.33

Thus

250/(x-20) = 250/(x) + 3.33

Solve again.

4. Originally Posted by delicate_tears
3) A tank can be filled with water by two pipes running together in 11_(1/9) minutes. If the larger pipe alone takes 5 minutes less to fill the tank than the smaller pipe, find the time that each pipe will take to fill the tank.
To learn the general technique for "combined work" exercises, try here.

Once you have learned the basic terms and techniques, the following should make sense:

. . .time to complete job (in minutes):
. . . . .smaller: s
. . . . .larger: s - 5
. . . . .together: 100/9

. . .portion completed (per minute):
. . . . .smaller: 1/s
. . . . .larger: 1/(s - 5)
. . . . .together: 9/100

Add their per-minute completion amounts, set equal to the total per-minute amount, and solve the rational equation. (The first step will be to multiply through to clear the denominators. Then you'll solve the resulting quadratic equation.)