Question

a train cover a distance vin 50 miniutes,if it run ai a Speed of 48km/hr on an average.find the speed at which vthe train must run to reduce the time of journey to 40 miniutes
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Answer 1

We are having time and speed given, So first we will calculate the distance. Then we can get new speed for given time and distance.

So let's solve it ,

$\\ \underline{\large\color{blue} \: {\sf Question :- }}$

A train cover a distance vin 50 miniutes,if it run ai a Speed of 48km/hr on an average.find the speed at which vthe train must run to reduce the time of journey to 40 miniutes ?

$\\ \\ \underline{\large\color{blue} \: {\sf Solution :- }}$

$\\ \\ \rm \: Time = \: \frac{50}{60} hr \: = \: \frac{5}{6} hr$

$\rm \: Speed \: = \: 48 \:mph \: (mph \: = metre \: per \: hour \: )$

$\rm \: Distance \: = \: s \: \times \: t \: = 48 \times \frac{5}{6} = 8 \times 5 = 40 \: km$

$\\ \\ \rm \: New \: time \: will \: be \: 40 \: minutes \: so,$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \: Time \: = \frac{40}{60} hr \: = \frac{2}{3} hr$

$\\ \\ \rm \: Now \: we \: know,$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \: Speed = \: \frac{distance}{time}$

$\\ \\ \rm \: New \: speed \: = 40 \times \frac{3}{2} \\ \\ \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: 20 \times 3 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \rm \underline{\boxed{ \rm \: 60mph \: }}$

$\\ \\ \red{ \bold{ Answer :-}}\underline{ \sf \: the \: speed \: at \: which \: the \: train \: must \: run \: to \: reduce \: the \: time \: of \: journey \: to \: 40 \: miniutes \: is \: 60 \: mph. }$