Answer:
a) Time until both vehicles meet is 1.5 hours after starting at noon. That makes it 1:30PM.
b) Average speed of car is 84 km/h
Explanation:
A -----------------------z------------B
Left Speed(km/h) Time
Car: 12PM X
Van: 12PM 60
Car/Van
DistanceCar AB + z
DistanceVan Az
Ratio: (AB+z)/Az = 7/5
Time until both meet = T (in hours)
Distance Car: xT
Distance Van: 60T
====
xT = AB + z
60T = Az
---
(xT/60T)= (7/5)
x = 60(7/5)
x = 84 km/h
=====
Time for car to reach B is: time (hr) = 108 km/(84 km/h)
time = 1.286 hours
Distance for at 1.289 hours is: distance (km) = (60 km/h)*(1.286 h)
distance = 77.14 km
At 1.286 hours, the car reverses direction. The van is (108 km - 77.14 km) or 30.86 km away.
Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours. The sum will be 30.86 km when they meet, at time of T.
Car Distance + Van Distance = 30.86 km
T(84 km/h) + t(60 km)
They meet when they are 0 km apart, which can be modeled with the following equation:
Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.
Let t be the time after 1.286 hours that both vehicles meet/collide.
t*(60 km/h) + t(84 km/h) = 30.86 km
t(60+84) = 30.86 km
t(144 km/h) = 30.86 km
t = 0.2143 hr
Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.
=================
a) Time until both vehicles meet is 1.5 hours after starting at noon. That makes it 1:30PM.
b) Average speed of car is 84 km/h
==============
CHECK
Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?
Car distance is (1.5 hr)(84 km/h) = 126 km
Van distance is (1.5 hr)(60 km/h) = 90.0 km
Ratio is 126/90 or 1.4
Ratio of 7/5 is 1.4
YES