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A boy goes to school with a speed of 3 km/hr, but he covers half distance then he remembers that he forgot the book at home so he goes back home with a speed of 5 km/hr. He takes 4 hrs for this process. How much speed should he increase to reach the school on time, If he normally takes 7 hrs to reach the school.

A boy goes to school with a speed of 3 km/hr, but he covers half distance then he remembers that he forgot the book at home so he goes back home with a speed of 5 km/hr. He takes 4 hrs for this process. How much speed should he increase to reach the school on time, If he normally takes 7 hrs to reach the school. Correct Answer 20/7 km/hr

Given:

Let the distance from home to school be 2x

Boy goes from home to school normal days = 7hrs

Concept:

In these types of questions, first find the distance between home to school then find the speed

Formula:

Distance = Speed × Time

Time = Distance/Speed

Calculation:          

From 1st condition,

Time taken by boy to cover home to half distance and half distance to home = 4hrs

⇒ (x/3) + (x/5) = 4

⇒ 8x/15 = 4

⇒ x = 15/2

So, distance from home to school = 2x = 15km

From 2nd condition

Boys normal days speed = 15/7 km/hr

Remaining hours he had to cover from home to school = 7 - 4 = 3 hrs

Now,

His today’s speed from home to school = 15/3 = 5km/hr

Speed increased by him = 5 - 15/7 = 20/7 km/hr

∴ Boy increases his speed to reach the school on time = 20/7 km/hr.

Alternate solution:

Distance = (S1 × S2 × total time)/ (S1 + S2)

In 1st condition we use formula, 

Half distance = 3 × 5 × 4/(3 + 5) = 15/2 km

Total distance from home to school = (15/2) × 2 = 15km

Normal speed by the boy when he goes from home to school = 15/7 km

Now remaining hours he have = 7 - 4 = 3 hrs

So speed = 15/3 = 5km/hr

Increase in speed = 5 - 15/7 = 20/7 km/hr

∴ Boy increase his speed to reach the school on time by = 20/7 km/hr

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