Math, asked by saisravani887, 9 months ago

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

Answered by amitnrw
2

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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