The distance from Melbourne to a railway station in Gippsland is 120 km. The average speed of one train is 9 km/h more than that of another train. The faster train takes 40 minutes less time for the trip. Let x km/h be the speed of the faster train.
a. give the speed of the slower train in terms of x.
b. give the time taken, in hours, for each of the trains to travel from melbourne to the gippsland station.
c. write an equation relating the two times.
2007-04-15 23:03:08 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
a)
The speed of the slower train is x - 9 km/h.
b)
The faster train takes
T = 120/x h to travel the distance.
The slower train takes
S = 120/(x - 9) h
c)
S = T + 40/60 h
120/(x - 9) = 120/x + 2/3
Just for fun, let's solve this!
120/x + 2/3 = 120/(x - 9)
Multiply both sides by 3x(x - 9)
360(x-9) + 2x(x-9) = 360x
360x - 3240 + 2x^2 - 18x = 360x
x^2 - 9x - 1620 = 0
x = [9 +/- sqrt(81 + 4*1620)]/2
x = 45 km/h (disregard negative value)
So the faster train travels at 45 km/h and takes
T = 120/45 = 2.666 h = 2 hours and 40 minutes
and the slower train travels at 36 km/h and takes
S = 120/36 = 3.333 h = 3 hours and 20 minutes.
2007-04-15 23:35:33 · answer #1 · answered by Robbie 1 · 0⤊ 0⤋
a) Since x is the speed of the faster train, and we're told it's 9 km/h faster than the other, then the speed of the slower train is just x - 9.
b) Speed is distance divided by time, so time is distance over speed. The two times would therefore be 120/x and 120/(x-9).
c) The time for the faster train was 40 minutes less, so subtracting 40 from the time of the slower train, we have:
120/x = 120/(x-9) - 40
2007-04-15 23:26:07 · answer #2 · answered by Anonymous · 0⤊ 0⤋
faster train=x time t-40/60 hours
slower train=x-9 time t hours
road=120 km.
120=x*(t-40/60)
120=(x-9)t
2007-04-15 23:14:35 · answer #3 · answered by iyiogrenci 6 · 0⤊ 0⤋
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2016-12-22 23:57:55 · answer #4 · answered by Anonymous · 0⤊ 0⤋
If something is 40% smaller, you purely subtract 40%. So 40% of 40 energy is sixteen: you are trying this by using multiplying 40 by using 0.4. the respond may well be 40 - sixteen = 24 A shorter way might merely be to multiply by using 40 by using 0.6, because of the fact it incredibly is a million-0.4.
2016-12-29 15:40:19 · answer #5 · answered by ? 3 · 0⤊ 0⤋