Question

On a 60 km stretch of road, a cyclist travels first 20 km at a uniform speed of 20 km/hr. how fast must he travel the remaining distance so that his average speed is 10 km/hr for the entire trip.

Answer 1

$Given: \\ Total \: \: distance =60km \\ Average \: speed \: of \: entire \: journey=20km/h \\ \\ Total \: Time \: taken = total \: distance/average \: speed =60/10 =6hr \\ Case :1 \\ \\ \\ Let us CALCULATE \\ \\ time taken \: \: to \: \: cover \: \: first \: \: 20km \: \: Speed=20km/h \\ Distance= \: 20km \\ T=distance/ speed=20/20 =1hr -equation ( 1) Case: 2$

$Let \: speed \: be =Xkm/h \\ X=40 \: KM/t \\ t=40/X hours ----equation( 2) \\ Total time = add equation 1 and 2 \\ =1 +40/X \\ Since total time =3 h \\ 6 =1 +40/X \\ 6-1 =40/X \\ 5 =40/X \\ X=8 km/h \\ Therefore \: cyclist \: should \: travel \: next 40 \: km \: distance \: \\ at \: a \: speed \: of \: 8 \: km/h.$

Answer 2

Answer

Therefore cyclist should travel next 40 km distance at a speed of 8 km/h.