Question

A boy covers 10km at a speed of 5kmph, 30km at a speed of 7kmph, 20km at a speed of 15kmpr. Find our average speed

Answer 1

Let,

=> a = 10 Km
=> b = 30 Km
=> c = 20 Km

and,

=> x = 5 km/h
=> y = 7 Km/h
=> z = 15 Km/h

Now,

=> <S> = Total Distance/Time taken

$= > S_{avg} = \dfrac{a + b + c}{ \frac{a}{x} + \frac{b}{y} + \frac{c}{z} }$
$= > S_{avg} = \dfrac{10 + 30 + 20}{ \frac{10}{5} + \frac{30}{7} + \frac{20}{15} }$
$= > S_{avg} = \dfrac{60}{2 + 4.2 + 1.3}$
$=> S_{avg} = \dfrac {60}{7.5}$

$=> S_{avg} = 8 \frac{m}{s}$

Answer 2

$\underline{\underline{\bold{SOLUTION:}}}$

Given that, the boy covers

10 km at a speed of 5 kmph,

30 km at a speed of 7 kmph and

20 km at a speed of 15 kmph

So, total time ( T ) taken by him

= $\frac{10}{5}+\frac{30}{7}+\frac{20}{15}$ hours

= $2 + \frac{30}{7} + \frac{4}{3}$ hours

= $\frac{(2*21)+(30*3)+(4*7)}{21}$ hours

= $\frac{42+90+28}{21}$ hours

= $\frac{160}{21}$ hours

and total distance ( X ) covered by him

= ( 10 + 30 + 20 ) km

= 60 km

∴ the average speed of the boy

= $\frac{\text{X}}{\text{T}}$ kmph

= $\dfrac{60}{\frac{160}{21}}$ kmph

= $\dfrac{60*21}{160}$ kmph

= $\dfrac{1260}{160}$ kmph

= 7.875 kmph