A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.a)30 km/hrb)40 km/hrc)50 km/hrd)60 km/hrCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Answer

Given : A train travels 360 km at uniform speed
If the speed had been 5km/h
Find : the speed of the train
solution : let uniform speed of train = x km/hr.
According to the given condition,
360/ x - 360/ x+5 = 1
= 360x + 1800- 360x = x² + 5x
= x² + 5x - 1800= 0
= x² + 45x - 40x - 1800 = 0
= x ( x + 45) - 40 (x + 45) = 0
= (x - 40) ( x + 45) =0
= x - 40 =0 or x+ 45= 0
= x = 40. or x = -45 ( rejected)
Hence, speed of the train 40 km/hr.
option ‘B' is correct...

Answer

To solve this problem, we can use the formula:

Distance = Speed × Time

Let's assume the original speed of the train is 'x' km/h. According to the question, if the speed had been 5 km/h more, it would have taken 1 hour less for the same journey.

1. Journey with the original speed:
Distance = 360 km
Speed = x km/h
Time = Distance / Speed = 360 / x hours

2. Journey with the increased speed:
Distance = 360 km
Speed = (x + 5) km/h
Time = Distance / Speed = 360 / (x + 5) hours

According to the given conditions, the time for the second journey is 1 hour less than the time for the first journey. So we can set up the equation:

360 / x - 360 / (x + 5) = 1

Now, let's solve this equation step by step:

Step 1: Multiply both sides of the equation by x(x + 5) to eliminate the denominators:
360(x + 5) - 360x = x(x + 5)

Step 2: Simplify the equation:
360x + 1800 - 360x = x^2 + 5x

Step 3: Combine like terms:
1800 = x^2 + 5x

Step 4: Rearrange the equation:
x^2 + 5x - 1800 = 0

Step 5: Factorize the quadratic equation:
(x - 40)(x + 45) = 0

Step 6: Set each factor equal to zero and solve for x:
x - 40 = 0 or x + 45 = 0
x = 40 or x = -45

Since speed cannot be negative, the only valid solution is x = 40 km/hr.

Therefore, the speed of the train is 40 km/hr, which is option B.

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