math for problem

Question

A train traveling at a speed of 20mph departs from Manhattan and heads towards New Jersey. At the same time, a train heading to Manhattan from New Jersey is departing at the same time, and will be going 40mph. If the two places are 120 miles apart, how far from New Jersey will the trains meet?E. 40 miles F. 60 miles G. 80 miles H. 100 miles

Answer 1

We will use the Distance formula:

Distance = rate * time

Distance for Manhatten train = 20t

Distance for New Jersey train = 40t

          D = 20t                                            D = 40t

I------- >--------------Meeting point---------------<-------------------I

Manhatten                                                           New Jersey

Train                                                                          Train

The total distance they are apart is 120 miles

I<------------------------------ 120 miles ------------------------------->I

We add the distances to get:

20t + 40t = 120

Solve for t:

60t = 120

t = 2 hours

They ask how far from New Jersey do they meet. That train’s distance is 40t, so plug in t=2:

40 (2) = 80 miles Answer

Answer 2

Use: D = R*T

D1 = (20)*T1 and D2 = (40)*T2

(120 - D) = (20)*T and D = 40*T

(120 - D)/20 = T and D/40 = T

T = T

(120 - D)/20 = D/40

40(120 - D) = D*20

4800 - 40D = 20D

4800 = 60D

80 = D

Distance = 80 miles.

Note; Let D = Distance the 2nd train traveled

because that's the distance we are looking for.

That's the distance from New Jersey to Manhattan.

The distance from Manhattan to NY is 120 - D.

Answer 3

Let d = the distance from New Jersey.

d = rt, so t = d/r, and the times are the same.

40/d = 20/(120 - d)

Cross multiply!

40(120 - d) = 20d

4800 - 40d = 20d

4800 = 60d

d = 80 miles