Question

Roshni cycles 2 kilometres at y km/h and then runs 4 kilometres at (y-4) km/h.
The whole journey takes 40 minutes.
(1) Write an equation in y and show that it simplifies to
y^2- 13y- 12-0​

Answer 1

Given that whole journey took 40 minutes,

convert minutes into hours 40/60 hours=2/3 hour,

T1+T2=2/3hour,

T1 is the time taken for first part of journey,

T2 is the time taken for second part of journey,

T1=2/y,

T2=4/(y-4),

2/y+4/(y-4)=2/3,

(2(y-4)+4y)/(y^2-4y)=2/3,

2(y-4+2y)*3=(y^2-4y)*2,

2 is cancelled on both sides,

(3y-4)*3=y^2-4y,

9y-12=y^2-4y,

y^2-13y+12=0.