Question

A woman met her friend at a coffee shop along the road. The friends spent so much time talking to one another that the woman was 24 minutes late to continue her journey. Her destination was 80km away, so she increased the speed by 10km/h and arrived at her meeting on time. What was the speed of her car before arriving at the coffee shop?

Answer 1

Let s=speed of the car on an interrupted journey. The time, t for the journey=80/s hours.

But t-24/60 hrs is the time she has left to do the journey at a speed of s+10, so t-0.4=80/(s+10).

Therefore 80/s-0.4=80/(s+10).

Multiply through by s(s+10): 80(s+10)-0.4s(s+10)=80s.

80s+800-0.4s^2-4s=80s, 0.4s^2+4s-800=0,

s^2+10s-2000=0=(s-40)(s+50) and s=40 kph.

Let's check. Time for uninterrupted journey=80/40=2 hrs.

Time for interrupted=80/50=1.6 hrs=1hr 36min, which is 24 mins short of 2 hours. So the time for the interrupted journey including the stop at the coffee shop is 1hr 36mins + 24 mins=2 hours.

Speed of the car was 40km/hr.