Question

Reena travels 15 km to her home partly by auto and partly by bus. She takes 1 hour if she travels 3 km by auto and the remaining by bus. On the other hand, if she travels 5 km by auto and the remaining by bus, she takes 10 minutes longer. Find the speed of the auto and bus.

Answer 1

Answer:

speed of auto is 2.5 km/he and speed of bus is 10 km/hr

Step-by-step explanation:

given data

total distance = 15 km

time auto = 1 hour

distance auto = 3 km

distance auto = 5 km

time longer = 10 min = 10/60 hour

to find out

speed of auto and bus

solution

we consider here speed of auto is = x km/hr

and speed of bus = y km/hr

so time equation will be

$\frac{3}{x} +\frac{15-3}{y} = 1$   .................a

and

$\frac{5}{x} +\frac{15-5}{y} = 1 +\frac{10}{60}$   .................b

to make simple we consider here 1/x = A and 1/y = B

3A + 2B = 1   .................c

and

5A + 10B =  $\frac{7}{6}$ .................d

so now equating equation c and d

3A + 2B  = 5A + 10B

-10B + 2B = 2A

A = -4B

so put in equation c

3(-4B) + 2B = 1

-12B + 2B = 1

B =  - $\frac{1}{10}$

and A = -4 ( - $\frac{1}{10}$ )

A = $\frac{4}{10}$

so we know

A =  $\frac{1}{x}$

$\frac{4}{10}$ =  $\frac{1}{x}$

x = 2.5

and

B =  - $\frac{1}{10}$ = $\frac{1}{y}$

y = -10

so speed of auto is 2.5 km/he and speed of bus is 10 km/hr