PLEASE HELP ME WITH THIS URGENT MATHS QUESTION I NEED HELP AND IM SO STUCK AHHHH?

2017-08-04 6:31 pm
Two trains, A and B are 300km apart. Two trains leave A and B simultaneously and proceed at constant speeds to the other station. The train from A reaches B 9 hours after the trains have met, and the train from B reaches the station A 4 hours after the trains have met. Find the speed of each train.

回答 (4)

2017-08-04 9:00 pm
✔ 最佳答案
let train 1 be from station A
let train 2 be from station B
let d1= distance train 1 travels after meeting train 2
let d2 = distance train 2 travels after meeting train 1
let r1 = rate of train 1
let r2 = rate of train 2
let t = time when trains meet
distance =rate * time or d = r * t

at meeting point train 1 has travelled r1 * t from A
and train 2 will travel 4 hours to get to station A or r2 * 4
r1 * t = r2 * 4
t = (r2 * 4)/r1
also:
r2 * t = r1 * 9
t = (r1 * 9)/r2
t = t
(r2 * 4)/r1 = (r1 * 9)/r2
4 (r2)^2 = 9 (r1)^2
r1 = (2/3) r2
then:
d1 + d2 = 300
4 * r2 + 9*r1 = 300
4 * r2 + 9*(2/3) * r2 = 300
4 * r2 + 6 * r2 = 300
10 * r2 = 300
r2 = 30 km/h
r1 = (2/3) * 30 = 20 km/h

I hope this helps.
2017-08-04 7:38 pm
Let a km/h be the speed of the train from A, and b km/h be that from B.

Distance traveled by the train from A after the trains have met = (a km/h) × (9 h)= 9a km
Then, distance traveled by the train from B before the trains have meet = 9a km

Distance traveled by the train from B after the trains have met = (b km/h) × (4 h) = 4b km
Then, distance traveled by the train from A before the trains have met = 4b km

Distance between A and B (in km) :
9a + 4b = 360
Then, 4b = 360 - 9a …… [1]

When the two trains meet,
Time taken for the train from A = Time taken for the train from B
4b/a = 9a/b
9a² = 4b²
Take square roots : 3a = 2b or 3a = -2b (rejected)
4b = 6a …… [2]

Substitute [2] into [1] :
6a = 360 - 9a
15a = 360
a = 24

Substitute a = 24 into [2] :
4b = 6 × 24
b = 36

Ans:
The speed of the train from A = 24 km/h
The speed of the train from B = 36 km/h

====
Check:
Time taken for the two trains to meet = 360 / (24 + 36) h = 6 h

Time taken for the train from A to reach B = 360 / 24 h = 15 h = (6 h) + (7 h)
Hence, 7 h after the two trains meet.

Time taken for the train from B to reach A = 360 / 36 h = 10 h = (6 h) + (4 h)
Hence, 4 h after the two trains meet.

The answers are checked to be correct.
2017-08-04 8:52 pm
a = speed of the train from A
b = speed of the train from B
t = time to meet = 300/(a+b)
300/a = 300/(a+b)+9,
300/b = 300/(a+b)+4
a = 20 km/h
b = 30 km/h
2017-08-04 6:33 pm
a 94km/h b 40km/h


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