A car and a bus starts from point A. After T hours bird is 48 km ahead of car, while after 8 hours distance between bus and car is same as distance covered by bus in one hour. If relative speed of car and bus if they move towards towards each other is 240, then how much distance can bus cover in (T-1/2) hours?
Answers
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Given,
A car and a bus start from point A.
The relative speed of the car and bus when they move towards each other = 240
To find,
Total distance covered by the bus in 1/2 hours.
Solution,
We can simply solve this numerical problem by using the following process:
Let us assume that,
The speed of the car is "x km/hr" (kilometers per hour)
The speed of the bus is "y km/hr" (kilometers per hour)
As per the principles of linear motion,
Speed (S) = Distance traveled (D) / Time taken(T)
Speed (S) = Distance traveled (D) / Time taken(T)I.e., Distance traveled (D) = Speed (S) x Time taken(T)
Now, as per the question,
Total distance traveled by bus in 8 hours - Total distance traveled by car in 8 hours = Total distance traveled by bus in 1 hour
=> 8y - 8x = y
=> 7y = 8x (Equation 1)
Also, as per the question,
The relative speed of the car and bus when they move towards each other = 240
=> x + y = 240 (Equation 2)
On solving equations 1 and 2, we get:
x + y = 240 (from Equation 2)
=> x + 8x/7 = 240 (from Equation 1)
=> 15x = 240*7
=> x = 16*7
=> x = 112
So from equation 2,
y = 240-x
= 240-112
=> y = 128
So, speed of the bus = 128 km/hr
So, the total distance covered by the bus in 1/2 hours = speed x time
= 128*1/2 km
= 64 km
Hence, the total distance covered by the bus in 1/2 hours is 64 kilometers.