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Question

Bob wanted to ride a bicycle from A at a speed of 12km/h which would let him be able to arrive at B on time. But delayed 20 mins, in the end, he had to 15km/hr and he arrived 4 mins earlier. What far were a and B Apart?

Answer 1

distance = rate x time

 

rate1 = 12 km/hr

t1 = number of hrs to travel D km (from A to B)

 

D = rate1*t1

 

rate2 = 15 km/hr

t2 = t1 - 4 min*(1 hr/60 min) = t1 - (1/15) hr  

t2 = t1 - 1/15

 

D = rate2*t2

 

Set D's equal to each other and solve for t1:

 

rate1*t1 = rate2*t2

 

rate1*t1 = rate2*(t1 - 1/15) 

rate1*t1 = rate2*t1 - (1/15)*rate2         (combine like terms and solve for t1)

 

t1*(rate1 - rate2) = -(1/15)*rate2

 

t1 = -(1/15)*rate2/(rate1 - rate2) = -(1/15)*15/(12 - 15) = -1/-3 = 1/3 hr

 

t1 = 1/3 hr

 

Plug into D = rate1*t1:

 

D = 12 km/hr*(1/3)hr = 4 km between A and B