Question

The 12:00 p.m. eastbound train left the station at a constant speed of 40 miles per hour. How can I find the distance travelled? I know that the formula is speed x time but I can't apply it here because of the time. Please help.

Answer 1

You cannot solve it....you would need a time and you are correct in stating that

d = speed * time

with only speed...we have 2 unknowns...and we cannot solve for distance

all you can do is make a generalized statement and say

the distance traveled is = 40 * how ever many hours they travel

d = 40t

Answer 2

This was my word problem: The 12:00 p.m. eastbound train left the station at a constant speed of 40 miles per hour. At 12:45 p.m., the next eastbound train left the station at a constant speed of 60 miles per hour. Assuming neither train stops along the way, how far apart will the two trains be at 2:00 p.m.?

Answer 3

I found the time for the second train which was 80 miles.

Answer 4

How do I find the distance for the first train then? =)

Answer 5

Okay, so you do know the time! The first train travels for 2 hours at 40 miles per hour, right?

Answer 6

oh crap. thank you! i was lost for some reason.

Answer 7

my bad!

Answer 8

The second train travels at 60 miles per hour. It starts at 12:45 PM and goes until 2 PM. How much time elapses? Multiply that by 60 miles per hour...

Answer 9

is the answer 10 miles?

Answer 10

Well, how far does each train travel?

Answer 11

First train goes 40 miles/hr * 2 hr = 80 miles
Second train goes 60 miles/hr * 1 1/4 hr = ?

Answer 12

my bad again! it's 80 mph because it'll be speed x time

Answer 13

no, not 80 mph....mph = miles per hour. neither train is going 80 miles per hour. one of the trains does go 80 *miles*, however

Answer 14

the second train will go 75 miles.

Answer 15

right! So how far apart are they at that point?

Answer 16

sorry i meant 80 miles.

Answer 17

another way to think of this problem is as two lines on a graph. The first train's position can be thought of as \(d_1= 40t\) if t is in hours. the second train's position can be thought of as \(d_2 = 60(t-0.75)\) if t is in hours.

Answer 18

now i figured it out. thank you.

Answer 19

then you plug in t = 2 in each equation to find out how far they've traveled, and subtract to get the distance apart.

another related problem would be to ask when the second train catches the first. the graphical representation here is very helpful — where the two lines cross is directly above the time value

Answer 20

My last "word problem" tip is to always, always check your answer to make sure it actually works :-)