Question

A car travels 30 km at a uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h. Find its average speed.​

Answer 1

$\huge\star\sf\underline\red{Solution:-}$

$\star\sf\underline\red{Given:} \\ \\ \sf\underline\red{Condition\:1st} \\ \\ \sf{Car\:travels\: Distance = 30 \:km\:at\:40\:km/h} \\ \\ \sf{Speed = 40km/h} \\ \\ \sf{Distance= 30 \:km} \\ \\ \sf{Time= ?}$

$\sf\green{We\: know\:that,} \\ \\ {\boxed{\sf{Speed = \dfrac{Distance}{Time} }}} \\ \\ \sf{So,} \\ \\ {\sf{40 = \dfrac{30}{Time} }}$

so,

${\sf{ Time = \dfrac{30}{40} hours}} \\ \\ {\sf{Time(t_{1}) = \dfrac{3}{4} hours }}$

$\sf\underline\red{Condition\:2nd:-} \\ \\ \sf{Speed = 20km/h} \\ \\ \sf{Distance = 30km} \\ \\ \sf{Time = ?} \\ \\ {\sf{20 = \dfrac{30}{Time} }}$

${\sf{Time = \dfrac{30}{20} hours }} \\ \\ {\sf{Time(t_{2}) = \dfrac{3}{2} hours }}$

$\sf\green{Total\: Time\:taken\:by\:Car,}$

${\sf{Total\:Time\: Taken = \dfrac{3}{4} + \dfrac{3}{2} hours}} \\ \\ \implies\sf{ \dfrac{3+6}{4} hours} \\ \\ \implies\sf{ \dfrac{9}{4} hours}$

$\sf\green{Total\: Distance\: Travelled = 30km + 30km} \\ \\ \implies\sf{60\:km}$

Now,

${\boxed{\sf{Average\:Speed= \dfrac{Total\: Distance\:Travelled}{Total\:Time\:Taken} }}} \\ \\ \implies\sf{ \dfrac{60 \times 4}{9} } \\ \\ \implies\sf{ \dfrac{240}{9} }$

$\implies\blue{\boxed{\sf{26.6\:km/h}}}$

thus,

$\sf\red{Average\: Speed\:of\:car\:is\: 26.6 \: Kilometres/hour}$

$\sf\underline\pink{Thanks}$

Answer 2

${\huge{\small{\bold{\red{Answer:-}}}}}$

26.67 km/hrs.

$\blue{Step\: by \:step \:explanation :-}$

${\huge{\underline{\small{\bold{\orange{we\:know\: that ,}}}}}}$

$Speed=Distance / time$

${\huge{\underline{\small{\bold{\blue{Therefore,\:}}}}}}$

Time =distance/ speed

$\green{let's\: see \:the \:first\:case,}$

$s \:= \:distance\: = 30\: km$

$v \:=\: speed\: =\: 40\: km/hr$

$t\: =\: time \:= \:30 / 40$

$=3/4 hrs$

$\orange{let's\: see \:the \: second\:case,}$

$s \:= 30\: km$

$v\: = 20\: km/hr$

$t \:= \:30 / 20$

$t \:= 3/2\: hrs$

$Avg.\: Speed \:=Total distance/ Total time$

$=(30 + 30) / (3/4) + (3/2)$

$=60 / ( 3 + 6 ) /4$

$=60 / 9 × 4$

$=20 / 3 × 4$

$=80 / 3$

$=26.67\: ( Approx. )$

${\huge{\small{\bold{\green{Hence,}}}}}$

Average speed of the car is 26.67 km/hrs ( Approx. )