Please help, I'm really bad at speed, time, distance math problems. No links, please.
Answers
Answer:
102.6 miles
Step-by-step explanation:
In this problem, the initial distance between the two trains is the distance between New York and Boston, so
d = 240 miles
We know that the average speed of train A is 60 mph, and that train A travels from Boston to New York, so we can write its velocity as
v_A=+60 mphv
A
=+60mph
At the same time, train B travels from New York to Boston, so its velocity will be negative (since it is going in the opposite direction).
Also, we know that the speed of train B is 3/4 that of train A, so we have:
v_B = -\frac{3}{4}v_A=-\frac{3}{4}(60) = -45 mphv
B
=−
4
3
v
A
=−
4
3
(60)=−45mph
So, velocity of train B is 45 mph towards Boston.
Taking Boston as zero position as reference, x = 0, the position of train A at time t can be written as
x_A(t)=v_At = +60 tx
A
(t)=v
A
t=+60t
While the position of train B at time t is
x_B(t)=d-v_B t = d-45 tx
B
(t)=d−v
B
t=d−45t
The two trains meet when they have same position, so when
x_A=x_Bx
A
=x
B
And so when
60t=d-45t60t=d−45t
Solving for t,
\begin{gathered}60t+45t=d\\105t=240\\t=\frac{240}{105}=2.29 h\end{gathered}
60t+45t=d
105t=240
t=
105
240
=2.29h
The position at which they meet is
x_A(2.29)=60\cdot 2.29=137.4 mix
A
(2.29)=60⋅2.29=137.4mi
However, this is the distance from Boston; so the distance from New York is:
d=240-137.4=102.6 mid=240−137.4=102.6mi