A man goes from A to B of 8a/7 km distance with a speed of 40 km/hr and from B to C of a km distance with a speed of y km/hr and the total time taken to cover the total distance between A and C is 26 hours. If the man covers the total distance between A and C with a speed of y km/hr, he takes 4 hours more. Find y km/hr.a)20 km/hrb)30 km/hrc)45 km/hrd)25 km/hre)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Total distance between A and C = 8a/7 + a = 15a/7 km

15a/7y = 26 + 4

15a/7y = 30

y = a/14 ---- (1)

8a/(7 * 40) + a/y = 26

a/35 + a/y = 26 ---- (2)

From (1) and (2),

a/35 + a/(a/14) = 26

a/35 + 14 = 26

a/35 = 12

a = 420 km

15 * 420/(7 * y) = 30

15 * 60/y = 30

y = 30 km/hr

Answer

To solve this problem, let's break it down into smaller parts.

Given:
Distance from A to B = 8a/7 km
Speed from A to B = 40 km/hr
Distance from B to C = a km
Total time taken from A to C = 26 hours

Step 1: Calculate the time taken from A to B
Using the formula: Time = Distance / Speed
Time taken from A to B = (8a/7) / 40 = (8a/7) * (1/40) = a/35

Step 2: Calculate the time taken from B to C
Using the formula: Time = Distance / Speed
Time taken from B to C = a / y

Step 3: Calculate the time taken from A to C with a speed of y km/hr
Total time taken from A to C = Time taken from A to B + Time taken from B to C
26 = a/35 + a/y

Step 4: Solve the equation for y
Multiply through by 35y to eliminate the denominators:
26 * 35y = 35y * (a/35) + 35y * (a/y)
910y = a + 35a
910y = 36a
y = 36a / 910
y = 4a / 91

Step 5: Simplify the expression for y
y = 4a / 91
y = (4/91) * a

Therefore, the speed of the man to cover the total distance between A and C is 4a/91 km/hr.

To find the answer in terms of y, we need to substitute the value of a in terms of y.
Given that the man covers the total distance between A and C with a speed of y km/hr, he takes 4 hours more.
So, we can write the equation as:
26 = a/35 + a/y + 4

Substitute the value of a in terms of y:
26 = (4a/91)/35 + (4a/91)/y + 4
26 = (4/91) * (a/35) + (4/91) * (a/y) + 4
26 = (4/91) * (a/35 + a/y) + 4

From Step 3, we know that a/35 + a/y = 26 - 4 = 22
Substitute this value in the equation:
26 = (4/91) * 22 + 4
26 = 88/91 + 4
26 = (88 + 364)/91
26 = 452/91

Now, solve for y:
y = (4a/91) = (4 * 452/91) = 16

Therefore, the speed of the man to cover the total distance between A and C is 16 km/hr, which is not one of the given options. So, the correct answer is None of these.

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