Question

suman travel from home for his school at 3 km per hour he reaches school 8 minutes late. if he travels at the rate of 4 km per hour he reachee school 12 minutes early. find the distance between his school and home?​

Answer 1

To find :

• Distance between Suman's school and home

Let :

• Distance between school and Home = x km
• time , she usually take to reach school = t hour

Given :

• if speed = 3km/h , t' = t hour + 8min
• if speed= 4km/h , t" = t hour - 12min

Solution :

In first case ,

• speed of 3km/hr
• t' = t + (8/60) hour

distance = speed × time

• x = 3( t + (8/60) ) ........ equation 1

In second case,

• speed = 4km/h
• t" = t + (12/60) hour
• x = 4 × (t - (12/60) ) ........ equation 2

equating equation 1&2

we get;

$3(t + \frac{8}{60} ) = 4(t + - \frac{12}{60} ) \\ \\ \implies \: 3t \: + \: \frac{3 \times 8}{60} \: = \: 4t \: - \: \frac{4 \times 12}{60} \\ \\ \implies \: 3t \: + \frac{24}{60} = 4t \: - \frac{48}{60} \\ \\ \implies \: 4t \: - 3t \: = \dfrac{24 + 48}{60} \\ \\ \implies \: t \: = \: \frac{72}{60}$

putting value of t in equation 1, we get

$x = 3 \times ( t + \frac{8}{60} ) \\ \\ x = 3 \times ( \frac{72}{60} + \frac{8}{60} ) \\ \\ x \: = \: 3 \times ( \frac{72 + 8}{60} ) \\ \\ x \: = \: \frac{3 \times 80}{60} \\ \\ x \: = \: \frac{240}{60} \\ \\ x \: = \: 4$

ANSWER :

• Distance between school and Home = 4km