3. Question 4
Three cars A, B and C travelled from Delhi to Mumbai along the same highway. The three cars
started at the same time, but Car B travelled at a speed 10 km/hr higher than A's speed and
arrived at Mumbai 1 hour before A's arrival. Car Carrived at Mumbai 33 33 minutes earlier
than A, travelling half the time at the speed of car A and the other half at the speed of car B.
Find the total distance covered by the three cars.
Answers
Given : Three cars A, B and C travelled from Delhi to Mumbai along the same highway. The three cars started at the same time, but Car B travelled at a speed 10 km/hr higher than A's speed and arrived at Mumbai 1 hour before A's arrival. Car Carrived at Mumbai 33 minutes earlier than A
To find : the total distance covered by the three cars.
Solution:
Let say Distance = D km
Speed of Car A = A km/hr
Speed of Car B = A + 10 km/hr
Time taken by Car A = T hr
Time Taken by Car B = T - 1 hr
AT = (A + 10) (T - 1)
=> AT = AT - A + 10T - 10
=> 10T = A + 10
Time take by Car C = (60 T - 33)/60 hrs
Half the time at the speed of car A and the other half at the speed of car B.
=> (A/2) ( (60 T - 33)/60) +( (A + 10)/2 ) (60 T - 33)/60) = AT
=> (A + 5) (60 T - 33)/60 = AT
=> (A + 5) (60 T - 33) = 60AT
=> (A + 5) (20 T - 11) = 20AT
=> 20AT + 100T -11A - 55 = 20AT
=> 100T = 11A + 55
10T = A + 10
=> 100T = 10A + 100
10A + 100 = 11A + 55
=> A = 45
10T = A + 10
=> 10T = 45 + 10
=> T = 5.5
AT = 45 * 5.5 = 247.5 km
Distance covered by each car = 247.5 km
total distance covered by the three cars. = 3 * 247.5
= 742. 5 km
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