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Saket travelled from home to a resort at a speed of 55 km/h. While returning via the same route, he got stuck in traffic and his travelling time extended by half an hour. The speed at which he was returning was 66 km/h. Find the total distance covered by him.
- a)242 km
- b)165 km
- c)330 km
- d)484 km
Correct answer is option 'C'. Can you explain this answer?
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Saket travelled from home to a resort at a speed of 55 km/h. While re...
Problem Analysis:
Saket travelled from home to the resort at a speed of 55 km/h. On his return journey, he got stuck in traffic and his travelling time increased by half an hour. The speed at which he was returning was 66 km/h. We need to find the total distance covered by him.
Solution:
Let the total distance covered by Saket be d km.
Let the time taken by Saket to travel from home to the resort be t1 hours.
Let the time taken by Saket to travel from the resort to home be t2 hours.
Given, the speed at which Saket travelled from home to the resort = 55 km/h.
Therefore, the distance travelled by Saket from home to the resort = 55t1 km.
Also, given that the speed at which Saket travelled from the resort to home = 66 km/h.
Therefore, the distance travelled by Saket from the resort to home = 66(t2 + 0.5) km.
Since Saket travelled the same distance both ways, we have:
55t1 = 66(t2 + 0.5)
55t1 = 66t2 + 33
11t1 = 22t2 + 11
t1 = 2t2 + 1
Substituting the value of t1 in terms of t2 in the above equations, we get:
55(2t2 + 1) = d
110t2 + 55 = d
d = 110t2 + 55
Therefore, the total distance covered by Saket is 110t2 + 55 km.
Option C, 330 km is the correct answer.
Saket travelled from home to the resort at a speed of 55 km/h. On his return journey, he got stuck in traffic and his travelling time increased by half an hour. The speed at which he was returning was 66 km/h. We need to find the total distance covered by him.
Solution:
Let the total distance covered by Saket be d km.
Let the time taken by Saket to travel from home to the resort be t1 hours.
Let the time taken by Saket to travel from the resort to home be t2 hours.
Given, the speed at which Saket travelled from home to the resort = 55 km/h.
Therefore, the distance travelled by Saket from home to the resort = 55t1 km.
Also, given that the speed at which Saket travelled from the resort to home = 66 km/h.
Therefore, the distance travelled by Saket from the resort to home = 66(t2 + 0.5) km.
Since Saket travelled the same distance both ways, we have:
55t1 = 66(t2 + 0.5)
55t1 = 66t2 + 33
11t1 = 22t2 + 11
t1 = 2t2 + 1
Substituting the value of t1 in terms of t2 in the above equations, we get:
55(2t2 + 1) = d
110t2 + 55 = d
d = 110t2 + 55
Therefore, the total distance covered by Saket is 110t2 + 55 km.
Option C, 330 km is the correct answer.
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Community Answer
Saket travelled from home to a resort at a speed of 55 km/h. While re...
He travelled both ways on the same route.
Let the distance of each side be A km.
His time difference for both sides will be half an hour.
Therefore, A/55 - A/66 = ½
A/330 = (1/2)
A = 165 km
Total distance = 2 x A = 2 × 165 = 330 km
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Saket travelled from home to a resort at a speed of 55 km/h. While returning via the same route, he got stuck in traffic and his travelling time extended by half an hour. The speed at which he was returning was 66 km/h. Find the total distance covered by him.a)242 kmb)165 kmc)330 kmd)484 kmCorrect answer is option 'C'. Can you explain this answer?
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