A cyclist traveled at a rate of 24 mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby town.
2006-07-08 19:11:16 · 4 answers · asked by Chris D 2 in Science & Mathematics ➔ Mathematics
Let the distance=d miles
Therefore, d/24+d/18=4.9
Solving it, d=50.4
So, the distance is 50.4 miles
2006-07-08 19:26:45 · answer #1 · answered by harunch2002 3 · 3⤊ 0⤋
let x be the distance between the towns.
time for first trip = x/24
time for second trip = x/18
.: x/24 + x/28 = 4.9 (hours)
simplifying.. (7x)/72 = 4.9
rearranging.. x = (72*4.9)/7 = 50.4 miles
2006-07-08 19:31:15 · answer #2 · answered by Alex 1 · 0⤊ 0⤋
v1 = 24mph
v2 = 18mph
v = s/t
s = vt (distance = velocity * time)
t1+t2 = 4.9 hours
s = s1 = s2 (assume same path to/from the town)
s = v1 * t1 = v2 * t2
t2 = 4.9 hours - t1
24 t1 = 18 (4.9 - t1)
24t1 = 88.2 - 18t1
24t1 + 18t1 = 88.2
42t1 = 88.2
t1 = 2.1hours
s = v1 t1 = 24 mph * 2.1 h = 50.4 miles
As a check...t2 = 4.9 - 2.1 = 2.8 hours
s = v2 t2 = 18 mph * 2.8 h = 50.4 miles (checks out)
2006-07-08 19:27:47 · answer #3 · answered by SkyWayGuy 3 · 0⤊ 0⤋
t1 = d / 24 => d = 24 * t1
t2 = d/18 => d = 18 * t2
24 * t1 = 18 * t2
t1 = (18/24) * t2 = (3/4 )* t2
t1+t2 = 4.9
(3/4) * t2 + t2 = 4.9
t2 * 1.75 = 4.9
t2 = 4.9/1.75
d = 18 * t2 = 18 * 4.9 / 1.75 = uhh ... arithmentic from here on out
2006-07-08 19:18:17 · answer #4 · answered by atheistforthebirthofjesus 6 · 0⤊ 0⤋