Marc left Town A at 8 a.m. and drove to Town B at an average speed of
60 km/h. 1 1/2 hours later, Ben left Town A and drove to Town B, follwing the
same route as Marc. After travelling for 240 km, Ben caught up with Marc.
(a) What was Ben's average speed?
(b) How far apart were they at 2 p.m.?
When Ben left Marc has already gone 1.5(60) or 90 km
Let the time taken for Ben to catch Marc be t hours
Total distance covered by Marc = 90 + 60t km
Total distance covered by Ben = 240 km
90 + 60t = 240
t = 2.5 hrs.
so Ben covered the 240 km in 2.5 hrs, so his speed was 96 km/h
at 2 pm, marc has gone for 6 hours, and he has travelled 360 km
at 2 pm, Ben has gone for 4.5 hrs, and he has travelled 4.5(96) or 432 km
they will be 72 km apart.
Let us assume that Ben’s average speed is VB.
Time taken by Marc to cover 240 km is,
t = (240 km)/(60 km/h) = 4 hr
Ben will cover 240 km in (4 - 1 1/2) hr = 2.5 hr
So, Distance covered by Ben = Distance covered by Marc
240 km = 240 km
VB * 2.5 = 240 km
VB = 96 km/h
So, Average speed of Ben is 96 km/h.
from 8 am to 2 pm Total hours = 6 hrs
Distance covered by Marc in 6 hrs is,
dm = 60 km/h * 6 h = 360 km
Distance covered by Ben in 6 hrs is,
db 96 km/h * 6h = 576 km
So, distance between them at 2 pm is,
db - dm = 576 - 360 = 216 pm
Thus, they will 216 km apart at 2 pm.