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At 8:20 a.m., Rima leaves for school on her bicycle. She arrives at school 8 minutes late if she travels at a speed of 10 km/h, but 10 minutes early if she travels at a speed of 16 km/h. What time does school start each day?

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9:00 AM

9:30 AM

10:00 AM

10:30 AM

answer is A.

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Detailed Solution

Given that, Rima arrives at school 8 minutes late if she travels at a speed of 10 km/h, but 10 minutes early if she travels at a speed of 16 km/h.
We know that the two variables

x and y

are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y

are two variables in inverse variations, then

x ∝ 1 y ⇒ x = k 1 y ⇒ x = k y,        where k is proportianality constant ⇒ x y = k .... (1)

Let’s assume that the total distance Rima travels is

x km .

And the total time taken to reach the school from home to school is

t min .

Since Rima arrives at her school 8 minutes late if she goes at a speed of 10 km/h.

∴ x = 10 t + 8 ...... 1

And Rima arrives at her school 10 minutes early if she goes at a speed of 16 km/h.

∴ x = 16 t − 10 ...... 2

Equating equation (1) and equation (2), we get

10 t + 8 = 16 t − 10 ⇒ 10 t + 80 = 16 t − 160 ⇒ 80 + 160 = 16 t − 10 t ⇒ 6 t = 240

⇒ t = 40 min

Since Rima left for school at 8:20 AM, therefore school start each day at

= 8 : 20 + 40 min = 9 : 00 A M .

Thus, school starts each day at 9:00 AM.
Hence, option (1) is correct.

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