SOLUTION: A train travelling from Ay town to Bee town meets with an accident after 1 hour. The train is stopped for 30 minutes, after which it proceeds at four-fifths of its usual rate, arri

Question 696510: A train travelling from Ay town to Bee town meets with an accident after 1 hour. The train is stopped for 30 minutes, after which it proceeds at four-fifths of its usual rate, arriving at Bee town 2 hours late. If the train had covered 80 miles more before the accident, it would have just been one hour late. What is the usual rate of the train?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Equation for normal trip from A to B is
(1)
In hr, the train covers
The train is stopped for 30 minutes
hrs have now passed
Now it's rate is for the remaining time of

The distance covered is
Now I have
(2)
So far I have 2 equations with 3 unknowns, so
I need 1 more equation
---------------------
If the train covered mi at rate = ,
it traveled

Now the trip takes hrs, so the rest of the trip takes

The train is stopped for 30 minutes, so
There is hrs left
The distance covered after the accident is then
, and
(3)
-----------------------------------
Substitute (1) into (2)
(1)
(2)
(2)
(2)
(2)
(2)
(2)
-------------
(3)
(3)
(3)
(3)
(3)
and since

(3)
(3)
The usual rate of the train is 16 mi/hr
check answer:
(1)
(1)
(1) mi
-----------------
(2)
(2)
(2)
(2)
(2)
(2) mi
-----------------
(3)
(3)
(3)
(3)
(3)
(3) mi
OK

RELATED QUESTIONS
Ok, my question is this: Train one leaves town A and moves in the direction of town B... (answered by mananth)

Hi A train after travelling 50km meets an accident and and after reducing 3/4 of its... (answered by mananth,ikleyn)

A passenger train travelling at 25km/hr is moving in the same direction as the truck (answered by mananth,josgarithmetic)

1. Arlene and Lito are travelling north in separate cars on the same highway. Arlene is... (answered by Boreal)

Mark left town P for town Q at 10am, travelling at a uniform speed of 75km/h. Jane left... (answered by ikleyn,greenestamps,MathTherapy)

1) Two trains X and Y enter at the same time a tunnel 1 Km. long at the opposite ends.... (answered by ankor@dixie-net.com)

A train running from A to B meets with an accident 50 miles from A, after which it... (answered by ankor@dixie-net.com)

Town A and B are 400 miles apart. If a train leave A in the direction of B at 50 miles... (answered by josgarithmetic)

Town A and B are 400 miles apart. If a train leaves A in the direction of B at 50 miles... (answered by Alan3354)