SOLUTION: Ms. Castillo boarded a bus bound for Baguio at exactly 4AM. After one and one-half hours, her husband followed driving the family car at 75 mph., assuming that the bus was travelli

Algebra ->  Test -> SOLUTION: Ms. Castillo boarded a bus bound for Baguio at exactly 4AM. After one and one-half hours, her husband followed driving the family car at 75 mph., assuming that the bus was travelli      Log On


   

Question 1133385: Ms. Castillo boarded a bus bound for Baguio at exactly 4AM. After one and one-half hours, her husband followed driving the family car at 75 mph., assuming that the bus was travelling at an speed of 50 mph, at what time would her husband’s car overtake the bus?

Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
distance=v*t
for bus, it is 50*t
for car, it is 75(t-1.5)
They are equal at overtaking
50t=75t-112.5
-25t=-112.5
t=4.5
8:30 am ANSWER
bus has gone 50*4.5=225 miles
car has gone 75*3=225 miles


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours that it takes husband's
car to catch up with the bus
+d+=+75t+ = distance in miles that husband travels
until he catches up with bus
+50%2A1.5+=+75+ mi = bus's head start in miles
-------------------------------------------------------
Equation for the bus:
(1) +75t+-+75+=+50t+
Equation for husband:
(2) +d+=+75t+
-----------------------------
(1) +25t+=+75+
(1) +t+=+3+
and
(2) +d+=+75%2A3+
(2) +d+=+225+ mi
-----------------------------
1.5 hrs after 4 PM is 5:30 PM
Husband travels for 3 hrs after that,
3 hrs after 5:30 is 8:30 which is
when husband catches up with bus
---------------------------------------
check:
In the time, +t+, bus travels
+225+-+75+=+150+ mi
+d%5B1%5D+=+50%2A3+ = also distance bus travels in the +t+
+d%5B1%5D+=+150+ mi
checks OK