SOLUTION: Two cars start at the same time from the same place and travel along the same road. Car A has a constant speed of 50mph. Car B travels with constant speed v for 100 miles then stop

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Question 666148: Two cars start at the same time from the same place and travel along the same road. Car A has a constant speed of 50mph. Car B travels with constant speed v for 100 miles then stops to rest for time t, then travels again with constant speed v for another 100 miles. Assume v is greater than 50mph.
A. Write algebraic expressions for the following:
(1) How far is B ahead of A when B stops to rest?
(2) Where is A when B starts up again?
(3) What time is it when A passes a marker 150 miles from the starting point?
(4) Suppose we were at the 150 mile marker. How long would we have to wait between the passing of A and the passing of B?
(5) Where is A when B arrives at a point 200 miles from it's starting point?
B.Suppose A and B arrive at the 200 mile position at the same time.
(1) write and equation that states this condition.
(2) How long does B rest if its speed is 60 mph?
(3) what must B's speed be if it rests for one hour?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two cars start at the same time from the same place and travel along the same road.
Car A has a constant speed of 50mph.
Car B travels with constant speed v for 100 miles then stops to rest for time t, then travels again with constant speed v for another 100 miles.
Assume v is greater than 50mph.
:
A. Write algebraic expressions for the following:
(1) How far is B ahead of A when B stops to rest?
100 - 50%28100%2Fv%29
:
(2) Where is A when B starts up again?
50%28%28100%2Fv%29%2Bt%29
:
(3) What time is it when A passes a marker 150 miles from the starting point?
150%2F50 = 3 hrs from start
:

(4) Suppose we were at the 150 mile marker. How long would we have to wait
between the passing of A and the passing of B?
3 - 150%2Fv
:
(5) Where is A when B arrives at a point 200 miles from it's starting point?
50%28%28200%2Fv%29%2Bt%29
:
;

B.Suppose A and B arrive at the 200 mile position at the same time.
(1) write and equation that states this condition.
It takes A: 200/50 = 4 hrs, to reach the 200 mi marker, therefore:
%28200%2Fv%29%2Bt = 4
:
(2) How long does B rest if its speed is 60 mph?
%28200%2F60%29%2Bt = 4
3.33 + t = 4
t = 4 - 3.33
t = .67 hrs, about 40 min
:
(3) what must B's speed be if it rests for one hour?
%28200%2Fv%29%2B1 = 4
%28200%2Fv%29 = 4 - 1
%28200%2Fv%29 = 3
3v = 200
v = 200/3
v = 66.67 mph