A bicycle rider travels 18 miles in the same amount of time that it takes a jogger to travel 10 miles. If the bicyclist goes 9.6 miles per hour faster than the jogger, how fast does each person travel?
show steps so i can understand
2007-10-17 22:01:14 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Do your own homework, figure it out and take some pride in yourself.
2007-10-17 22:03:00 · answer #1 · answered by Anonymous · 1⤊ 1⤋
Distance is equal to rate by time, thus both travel for an unknown time x. Assume the jogger is moving at y mph.
So for the bicycle rider moving 9.6mph faster:
(9.6+y)x=18
and the jogger moving at y mph:
y(x)=10.
x and y are equal in both equations, so solve for x in both:
x=18/(9.6+y) and
x=10/y
set the equations equal to each other:
18/(9.6+y)=10/y
Solve for y:
18y=10(9.6+y)
18y=96+10y
8y=96
y=12
y was assumed to be the joggers speed given in mph. Thus the jogger is moving at 12 mph. The bicyclist is moving 9.6 mph faster, thus the bicyclist is moving at 21.6 mph (12+9.6)
hope that helped!
2007-10-18 05:09:57 · answer #2 · answered by Not Quite Agnostic 2 · 0⤊ 0⤋
1. Let S1 represent the speed of the cycler.
Let S2 represent the speed of the jogger.
2. In the same amount of time (let's call that T), they travel their respective distances. Speed multiplied by time is the distance,
distance of cycler: S1 * T = 18 miles
(solve for T, T = 18/S1)
distance of jogger: S2 * T = 10 miles
(solve for T, T = 10/S2)
Since both times are the same (T),
18/S1 = 10/S2.
or solve for S1,
18 = S1*10/S2
S1 = S2*18/10
S1 = S2 *1.8
3. The bicyclist goes 9.6 miles per hour faster than the jogger is expressed as:
S1 = S2 + 9.6
Using the releation obtained S1 = S2*1.8
Then S2 * 1.8 = S2 + 9.6
4. Solving for S2,
S2 * 1.8 - S2 = 9.6
S2 (1.8 - 1) = 9.6
S2 * 0.8 = 9.6
S2 = 9.6 / 0.8
S2 = 12 miles per hour
Solving for S1 using S1 = S2*1.8
S1 = 12 * 1.8
S1 = 21.6 miles per hour
5. Answer: Therefore, the cycler travels 21.6 miles per hour, and the jogger travels at 12 miles per hour.
6. Check:
S1 = S2 + 9.6
21.6 = 12 + 9.6
21.6 = 21.6
2007-10-18 05:20:52 · answer #3 · answered by markedchicken 2 · 0⤊ 0⤋
Let t = time of travel of both in hour.
=> speed of cyclist = 18/t miles/hour
and speed of jogger = 10/t miles/hour
Now 18/t = 9.6 + 10/t
=> 18 = 9.6t + 10
=> t = 8/9.6 hour
=> speed of cyclist = 18/t = 18*9.6/8 = 21.6 miles/hour
and speed of jogger = 10/t = 10*9.6/8 = 12 miles/hour
Verification: Difference is 9.6 miles/hour.
2007-10-18 05:14:20 · answer #4 · answered by Madhukar 7 · 0⤊ 0⤋
both the bicycler n jogger covers the dist 18 and 10miles in same time...let it be= ´X´hr
so speed of the bicycler= (18/X)miles per hr
speed of the jogger= (10/X)miles per hr
so, bicycler goes [(18-10)/X]miles per hr faster than jogger..
now equate the above equation with the given data...
implies,
X=(1/1.2) implies, they both traveled the dist in 50min..
bicycler travels 18miles in 50min
so
cycler will cover 21.5miles per hour
lly jogger will cover 12 miles per hour
2007-10-18 05:23:41 · answer #5 · answered by ice_land_1988 1 · 0⤊ 0⤋
_________time_____distance____speed
Biker _____t________18________s
Jogger____t________10______(s - 9.6)
t = 18 / s
t = 10 / (s - 9.6)
18/s = 10 / (s - 9.6)
18(s - 9.6) = 10s
18s - 172.8 = 10s
8s = 172.8
s = 21.6
Biker : 21.6 mph
Jogger : 12 mph
2007-10-19 03:10:21 · answer #6 · answered by Como 7 · 0⤊ 0⤋
ohhhh dude, ....... owwww, gave me brainfreeze with that one. just go see some geek in ur class or something man.
2007-10-18 05:08:42 · answer #7 · answered by Lord Deimos 1 · 0⤊ 0⤋
i hate math
2007-10-18 05:04:05 · answer #8 · answered by Mallory 2 · 0⤊ 1⤋
Dude...google has everything!
2007-10-18 05:03:44 · answer #9 · answered by frida_fan66 2 · 0⤊ 1⤋