Question

a cyclist covers a distance of 10 km at the speed of 15 km/hr and other 15 km at the speed of 12km/hr. find his average speed for the whole journey​

Answer 1

GIVEN :–

• Cyclist covers a distance of 10 km at the speed of 15 km/hr .

• Cyclist covers a distance of 15 km at the speed of 12 km/hr.

TO FIND :–

• Average speed for the whole journey = ?

SOLUTION :–

▪︎ According to the first condition –

=> Distance = 10 km , Speed = 15 km/hr

• We know that –

$\\ \longrightarrow { \boxed{ \sf Speed = \dfrac{Distance}{time} }}$

• So that –

$\\ \implies \sf 15 = \dfrac{10}{time}$

$\\ \implies \sf time = \dfrac{10}{15}$

$\\ \implies{ \boxed{ \sf time = \dfrac{2}{3} hr}}$

▪︎ According to the second condition –

=> Distance = 15 km , Speed = 12 km/hr

• Using formula –

$\\ \implies \sf 12 = \dfrac{15}{time}$

$\\ \implies \sf time = \dfrac{15}{12}$

$\\ \implies{ \boxed{ \sf time = \dfrac{5}{4} hr}}$

$\\ \: \: \: \sf { \huge{.}} \: \: Hence \: ,\: Total \: \: time =\dfrac{5}{4} + \dfrac{2}{3} = \dfrac{23}{12} \: hr$

$\\ \: \: \: \sf { \huge{.}} \: \: And \: \: Total \: \: distance =10 + 15=25 \: km$

$\\ \: \: \: \sf { \huge{.}} \: \: So \: \: that \:, \: Average \: \: Speed = \dfrac{Total \: \: distance}{Total \: \: time}$

$\\ \implies \sf Average \: \: Speed = \dfrac{25}{ \left( \dfrac{23}{12} \right) }$

$\\ \implies \sf Average \: \: Speed = \dfrac{25 \times 12}{23}$

$\\ \implies \sf Average \: \: Speed = \dfrac{300}{23}$

$\\ \implies \large { \boxed{ \sf Average \: \: Speed = 13.04 \: \: \dfrac{km}{hr} }}$

Answer 2

$Distance (x1) = 10km</p><p>\\ Speed (y1) = 15kmh</p><p>\\ Time = \frac{Distance}{Speed} </p><p>\\ t1 = \frac{x1}{y1} = \frac{10}{15} </p><p> \\ t1= \frac{2}{3}h </p><p>\\ Distance(x2) = 15km</p><p>\\ Speed (y2) = 12kmh </p><p>\\ t2 = \frac{x2}{y2} = \frac{15}{12} </p><p>\\ t2 = \frac{5}{4} h</p><p>\\ Average \: Speed = \frac{Total \: Distance}{Total \: Time \: Taken} </p><p>\\ Average \: Speed = \frac{x1 + x2}{t1 + t2} </p><p> \\ Average \: Speed = \frac{10 + 15}{ \frac{2}{3} + \frac{5}{4} }</p><p>\\ Average \: Speed = \frac{25}{ \frac{8 + 15}{12}}</p><p> \\ Average \: Speed = \frac{25} {\frac{23}{12}} </p><p>\\ Average \: Speed = \frac{300}{23} kmh</p><p>\\ \boxed{\red{Average \: Speed = 13.04 kmh} }$