Question

Ram and bharat travel the same distance at the rate of 6 km per hour and 10 km perhour respectively. if ram takes 30 minutes longer than bharat, the distance travelledby each is

Answer 1

Let the distance traveled be x km 
TIME = DISTANCE / SPEED 
TIME = x / 6 - x/10 = 1/2 
MULTIPLY BY 30 
5x - 3x = 15 
2x = 15 
X = 7.5 km ANSWER 
CHECK 
7.5 /6 = 1.25 hours 
7.5/10 = 0.75 hours 
SUBTRACT = 0.50 hours = 30 minutes
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Answer 2

Distance is same
Hence, Speed is inversely proportional to time
Speed: 6 km/hr(Ram)---- 10 km/hr(Bharat)
Speed ratios: 6: 10--- 3:5
Time ratios(inverse)-- 5(Ram) : 3(Bharat)
Given time taken by Ram is 30 mins longer
Hence ratio difference== 30 mins or 1/2 hours
2=== 1/2
1 part = 1/4
Hence 5== 5*1/4 = 5/4 hours
Distance = Speed * Time
Time(Ram) = 5/4 hrs...Speed(Ram) = 6 km/hr
Distance = 6 * 5/4 = 7.5 Km
Hope it helps.