SOLUTION: 2 trains, A and B travelling at a constant speeds left 2 different stations 640km apart. Train A started at noon and train B at 1pm. Travelling on parallel tracks towards each othe

Question 243046: 2 trains, A and B travelling at a constant speeds left 2 different stations 640km apart. Train A started at noon and train B at 1pm. Travelling on parallel tracks towards each other, they passed each other at 4pm. If train A travelled at a speed of x km/h and train B was 20km/h slower than train A,
(i) write an expression, in terms of x, for the speed of Train B
(ii)write an expression, in terms of x, for the distance covered by train A just before it passed train B
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Fundamentally, this is a distance equation, so w start with D = RT as our basic distance equation.
Train A setup:
D = 640 - distance travelled by Train B
R = x
T = 4 hrs when it passes Train B coming from the opposite direction.
Train B setup:
D = 640 - distance travelled by Train A
R = x - 20
T = 3 hrs when it passes Train A coming from the opposite direction
(i) Speed of Train B = x - 20
(ii) Distance travelled by Train A = 4x
Since the moment they pass each other they have covered the 640 km distance. We can take our solution farther by substituting what we know.
4x + 3(x-20) = 640
4x + 3x - 60 = 640
7x = 700
x = 100
So Train A is going 100 km/hr.
We are told Train B is going 20 km/hr slower, so it is going 80.
We can check the solution by substituting these values. And we can calculate answers to questions that have not (yet) been asked.
Train A ran 100 km/hr for 4 hrs, so it had travelled 400 km at the moment it passed Train B.
Train B ran 80 km/hr for 3 hrs, so it travelled 240 km at the moment it passed Train A.
When they pass each other, their combined distance travelled logically has to be 640, which it is.
So, we're done.
RELATED QUESTIONS
Two train stations, A and B, are 300km apart. Two trains leave A and B simultaneously and (answered by josmiceli)

A freight train and a passenger train are in stations 540km apart. The freight train... (answered by josgarithmetic,ikleyn,MathTherapy)

Towns A and B are 540km apart. A train leaves A and travels to B at a constant speed. A... (answered by ankor@dixie-net.com)

At the same time but at different speeds, two trains, X and Y, leave from different... (answered by ankor@dixie-net.com)

.Two trains are travelling between two stations at a constant speed of 25kmph.The... (answered by ankor@dixie-net.com)

Two trains stations are 1250km apart. At midnight a passenger train and a freight train... (answered by josgarithmetic)

2 trains left the same station at the same time. Train A traveled north at 28mph and... (answered by mananth)

a northbound train left the station at noon. 2 hours later a southbound train left the... (answered by checkley75)

The distance between 2 stations a and b is 200 km .2 trains start at the same time from... (answered by josgarithmetic)