Susan left her home at 7 AM, driving her car at the rate of 45 mph. At 9 AM her sister Marion drove after her along the same highway, traveling at the rate of 60 mph. In how many hours will Marion pass Susan?
2007-08-01 11:40:04 · 8 answers · asked by Marriot_Plum23 1 in Science & Mathematics ➔ Mathematics
A 2-hour head start at 45mph = 90 miles.
Marion is going 15mph faster, so it will take her 90/15 = 6 hours to catch up.
You can do it all with equations, though I find the above way easier:
s = 45 (t + 2) // Susan's distance t hours after Marion starts
m = 60 t // Marion's distance
They meet when s=m:
45(t+2) = 60t
90 = 15t
6 = t
2007-08-01 11:46:00 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
When Marion starts, Susan is already 2 x 45 = 90 miles ahead of her. Marion's relative speed to Susan is 60 - 45 = 15mph, which means that in 1 hour, Marion will reduce the distance by 15 miles. So, Marion and Susan will meet after 90 / 15 = 6 hours, after which Marion will take the lead. That is, if they don't crash/hit something/get pulled over/stop to go to the bathroom ;)
2007-08-01 18:45:37 · answer #2 · answered by Shadow 3 · 0⤊ 0⤋
Susan drives T hours at 45 mph for a distance of 45T
Marion drives T-2 hours at 60 mph for a distance of 60(T-2)
When the distances are the same
45T = 60(t - 2)
45T = 60T - 120
-15T = - 120
T = 8
This is Susan's total time - Marion will pass in 8-2 or 6 hours
2007-08-01 18:49:27 · answer #3 · answered by kindricko 7 · 0⤊ 0⤋
let t be the time Susan leaves since 7 am. At 9 pm, or t - 2, is the time Marion leaves
distance = speed * time
Susan:
d = 45t
Marion:
d = 60 (t - 2)
when Marion passes Susan, they are at a same position
Susan = Marion
45t = 60(t - 2)
45t = 60t - 120
-15t = -120
t = 8 hrs
So, Marion will passes Susan in 8 - 2 = 6hrs
2007-08-01 18:48:14 · answer #4 · answered by 7 · 0⤊ 0⤋
Marion is catching up at the rate of 15 mph, and leaving 2 hours after, Susan is thus 90 mile away.
The gap will thus take 90/15 = 6 hours to reduce to zero, it will thus be 3 PM when Marion passes Susan.
Unless one of them stops on the way...
2007-08-01 18:46:54 · answer #5 · answered by Vincent G 7 · 0⤊ 0⤋
distance = rate X time
by the time Marion leaves Susan will have traveled for 2 hours
distance = (2 hours)*(45mph)
= 90 miles
60x = 90 + 45x (45x since susan is still going)
x is the amount of time (unknown) muliplying it by the rate would give you the distance, solving that equation would give you the x (the time in hours since it is mph) at which they are at the same distance
15x = 90
x = 6 hours
2007-08-01 18:52:24 · answer #6 · answered by π∑∞∫questionqueen 3 · 0⤊ 0⤋
the answer is in 6 hrs they will be at the same place so u figure the rate of both speeds the at 6 hrs and 10 secs mark marion will actually pass susan
2007-08-01 18:50:06 · answer #7 · answered by rockntaz 3 · 0⤊ 0⤋
Susan
1 hour - 45 miles
2 hours - 90 miles
3 hours - 135 miles
4 hours - 180 miles
5 hours - 225 miles
6 hours - 270 miles
7 hours - 315 miles
8 hours - 360 miles
9 hours - 405 miles
Marion
1 hour - 0 miles
2 hours - 0 miles
3 hours - 60 miles
4 hours - 120 miles
5 hours - 180 miles
6 hours - 240 miles
7 hours - 300 miles
8 hours - 360 miles
9 hours - 420 miles
2007-08-01 18:53:24 · answer #8 · answered by Anonymous · 0⤊ 0⤋