A runner is training by sprinting up a long hill then slowly jogging down. He runs uphill at 240 meters per minute and comes back down at 160 meters per minute. If one trip up the hill and back down takes 30 minutes, how far is a one way trip? CAN SOMEONE PLEASE HELP ME WITH THIS???
2006-07-03 16:23:30 · 8 answers · asked by Fairy_Dreamz 1 in Science & Mathematics ➔ Mathematics
Assume that the one way trip is x meters. So while the runner is going up, it takes x/240 minutes and while coming down it takes x/160 minutes.
Given that the total time taken is 30 minutes
So x / 240 + x/160 = 30
or, 2x/480 +3x/480 = 30
or, 5x/480 = 30
or, 5x = 30X480
or x = 5X6X480/5 = 6X480 = 2,880 meters.
So one way trip is 2,880 meters (or 2.88 kilometers) long .......
2006-07-03 16:40:04 · answer #1 · answered by TJ 5 · 2⤊ 0⤋
Let,
d = one way distance
t1 = d/240 = Time up the hill
t2 = d/160 = Time down the hill
Then,
t1 + t2 =30 min
d/240+ d/160 = 30 min
d/96 = 30 min
d = 2880 meters
2006-07-03 17:16:12 · answer #2 · answered by mgurreri01 1 · 0⤊ 0⤋
Remember that distance=velocity * time, thus T=D/V. If D=the distance up the hill, then T=D/(240 m/min) + D/(160 m/min). T=30 min, so 30=D/240+D/160 â 480*30=2D+3D â 14400=5D â D=2880 meters.
2006-07-03 16:36:47 · answer #3 · answered by Pascal 7 · 0⤊ 0⤋
time up + time down = 30 [minutes] --------->
u + n = 30 [minutes]
distance up = distance down = d [meters]
u [minutes] = d [meters] / 240 [meters/minute]
n [minutes] = d [meters] / 160 [meters/minute]
d = 240 u
d = 160 n
240 u = 160 n
u = (2/3)n
u + n = 30 [minutes] or
(2/3)n + n = 30
(5/3)n = 30 and n =18 [minutes]
Since
n [minutes] = d [meters] / 160 [meters/minute]
18 [minutes] = d [meters] / 160 [meters/minute]
d [meters] = 18 [minutes] * 160 [meters/minute]
d = 2880 meters (up or down the hill)
The whole trip is twice that or 5760 meters
2006-07-03 16:34:34 · answer #4 · answered by Anonymous · 0⤊ 0⤋
240 x = 160y
Y + X = 30
2006-07-03 16:31:37 · answer #5 · answered by balans_99 2 · 0⤊ 0⤋
I shall help you my fren...
>>>First we shall find the time taken for the trip upwards...
Form an equation.. Take the time upwards as t... Knowing the distance upwards is equivalent to distance downwards...
distance = speed x time...
240t = 160(30-t)
240t = 4800 - 160t
240t + 160t = 4800
400t = 4800
t = 12min
>>>Now you can find the distance of one-way trip...
distance = speed x time
=240m/min x 12min = 2880m = 2km 880m...
Cheers... (",)
2006-07-03 16:41:22 · answer #6 · answered by Ellusive Lady 3 · 0⤊ 0⤋
proof:
Length of trip in meters = ((240m/m+160m/m)/2) x 30 Minutes
Now you use a calculator on that.
2006-07-03 16:29:34 · answer #7 · answered by John Luke 5 · 0⤊ 0⤋
Velocity is meters/second.
Figure it out.
2006-07-03 16:27:06 · answer #8 · answered by TheAnomaly 4 · 0⤊ 0⤋