Question

if a skylist had gone 3 km per hr faster he would have taken 1 hr and 20 minutes less to ride a distance of 80 km find the time taken by him and the speed of the cycle and time consumed by him to cover the distance
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Answer 1

Answer:

Let the speed be “x” km/hr

Let the time taken be “y” hours

Total Distance=80kms

So,Speed=Distance/Time

=> x=80/y ; also y=80/x ; also xy=80

Now,as per the question time taken when the speed is increased by 3km/hr reduces by 1hr 20 minutes…

So, “80/x-80/(x+3) =4/3”

{80/x is the original time taken

80/(x+3) is the time taken when speed is increased by 3km/hr

1hr 20mins is nothing but 4/3 hour}

80/x - 80/(x+3) =4/3

[80(x+3) -80(x)] /x(x+3) =4/3

80(x+3) -80(x)=4/3 (x^2 +3x )

80x+240–80x=4/3 (x^2 +3x )

240=4/3 (x^2 +3x )

720=4 (x^2 +3x )

4x^2 +12x-720 =0

x^2 +3x -180 =0

solving the quadratic equation,

(x +15)(x-12) =0

So,x=-15 or x=12

since speed can’t be negative,x=12

So,speed=12km/hr

henceforth,time taken=y=Distance/speed=80/12 =6.66= 6 2/3=6 hr 40 mins

So,the cyclist took 6hr 40 mins for that ride!