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A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey.?
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A person travels the first one-fourth of his journey time at 80 kmph ,...
Problem:
A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey?
Solution:
Step 1: Find the distance travelled at 80 kmph
Let us assume that the total distance travelled by the person is 'd'.
As per the problem, the person travels the first one-fourth of his journey time at 80 kmph.
Let the distance travelled at 80 kmph be 'd1'.
Therefore, d1 = (1/4) * d
Given, speed = 80 kmph and time = (1/4)th of the total time taken for the journey.
Using the formula, Speed = Distance / Time, we can calculate the time taken for the first one-fourth of the journey.
Time taken = Distance / Speed
Time taken = d1 / 80
Time taken for the remaining distance = Total time taken - Time taken for the first one-fourth of the journey.
Time taken for the remaining distance = (3/4)th of the total time taken for the journey.
Time taken for the remaining distance = (3/4) * Total time taken
Step 2: Find the distance travelled at 60 kmph
Let the distance travelled at 60 kmph be 'd2'.
Using the formula, Speed = Distance / Time, we can calculate the distance travelled at 60 kmph.
Speed = 60 kmph and Time = Time taken for the remaining distance.
60 = d2 / [(3/4) * Total time taken]
d2 = 60 * [(3/4) * Total time taken]
Therefore, Total distance travelled = d1 + d2 = (1/4)d + 60 * [(3/4) * Total time taken]
Step 3: Find the Total time taken
Using the formula, Speed = Distance / Time, we can calculate the Total time taken for the journey.
Speed = Total distance travelled / Total time taken
260 / Total time taken = (1/4)d / 80 + 60 * [(3/4) * Total time taken]
260 / Total time taken = (1/320)d + (45/2) * Total time taken
260 = (1/320)d * Total time taken + (45/2) * (Total time taken)^2
45(Total time taken)^2 - 520(Total time taken) + 640 = 0
Solving the above quadratic equation, we get Total time taken = 28/3 hours or 9.33 hours.
Community Answer
A person travels the first one-fourth of his journey time at 80 kmph ,...
65 kmph
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A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey.?
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A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey.?.
A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person travels the first one-fourth of his journey time at 80 kmph ,and the remaining at 60 kmph .If he covers a total distance of 260 km ,find average speed over the entire journey.?.
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