Cities A and B are joined by a 351-mi long railroad line. One train leaves City A and another leaves City B at exactly the same time, heading toward each other. If the A train is moving at 55 mph and B train is averaging 62 mph, when will the two trains pass each other?
2006-07-30 18:17:17 · 18 answers · asked by DohDoh 1 in Science & Mathematics ➔ Mathematics
THIS IS NOT MY HOMEWORK!!! I just saw this in one of those "Test Your IQ" books. I already solved this problemand got the right number but using a different method which no one has used here. I still don't get why the rate is "55+62"? Can anyone explain?
2006-07-30 18:53:13 · update #1
3 hours
D = R*T
351 = (55 + 62)*T
T = 3
2006-07-30 18:21:00 · answer #1 · answered by bogusman82 5 · 0⤊ 0⤋
3
2006-07-31 01:31:21 · answer #2 · answered by ping_er_18 1 · 0⤊ 0⤋
You know the formula
d = rt
distance = rate x time
Given,
351 mi = total distance
55 = rate of train A
62 = rate of train B
Since they start exactly at the same time, then their "time" are equal. If we let x = the time it takes for them to meet.
x = time of train A
x = time of train B
55x = distance of train A(d = rt)
62x = distance of train B
since the total distance is 351 mi, then
55x + 62x = 351
117x = 351
117x/117 = 351/117
x = 3 hours
Check:
After 3 hours, train A with rate 55 mi/hr has traveled
3(55) = 165 miles
After 3 hours, train B with rate 62 mi/hr has traveled
3(62) = 186 miles
Total = 351 miles
^_^
2006-07-31 07:08:32 · answer #3 · answered by kevin! 5 · 0⤊ 0⤋
Lets us assume that the two train will pass each other at point x.
therefore the time taken for A to pass x is x/55
time taken for b to pass this point is 351 - x / 62
x/55 = (351 - x) / 62
or,62x = 55 (351 - x)
or,62x = 19305 - 55x
or, 117x = 19305
or, x = 165m
therefore, the time is 165 / 55 = 3 hours after the journey has started
2006-07-31 03:36:16 · answer #4 · answered by Iluvharrypotter_tonima 2 · 0⤊ 0⤋
To see why you add 62 and 55:
The distance between the trains at any time t is:
351 - (distance traveled by A train) - (distance traveled by B train)
And you need to know when the distance between them is 0:
351 - dA - dB = 0
Using the DiRT formula:
351 - rA*t - rB*t = 0
Now use the Distributive Property:
351 - t(rA + rB) = 0
Now solve this equation to find t = 3.
2006-07-31 02:47:00 · answer #5 · answered by Katie S 1 · 0⤊ 0⤋
Not allowing any time for acceleration or the size of the train, 3.0 hours after they leave.
351/(55+62) = 3
...but you should really consider doing your own homework!
2006-07-31 01:23:30 · answer #6 · answered by minefinder 7 · 0⤊ 0⤋
this is a simple t=d/r problem (time = distance/rate)
The Distance is 351 mi.
The rate, since they are moving towards each other, is the sum of their averages, which is 55 + 62 = 117 mph
time = distance/ rate
time = 351mi/(117 mi/hr)
time = 3 hrs
Therefore after three hours, they pass each other
2006-07-31 02:44:51 · answer #7 · answered by Brian F 4 · 0⤊ 0⤋
62+55=117 (average speed of trains realtive to each other)
351/117 = 3 hours (after this time the distance between them will become 0, so they will meet)
2006-07-31 01:21:32 · answer #8 · answered by Synaps 2 · 0⤊ 0⤋
In 3 hours
2006-07-31 01:21:35 · answer #9 · answered by Michael M 6 · 0⤊ 0⤋
d=rt; d=351;
rate of A train =55; rate of B train=62
Since what is asked is the time they will pass each other, time must be constan (they left at the same time).
351=55t+62t; 117t=351; t=3.
They will meet in 3 hours.
2006-07-31 02:35:07 · answer #10 · answered by *DeaD* 2 · 0⤊ 0⤋