Skip to main content

King's Maths School

Challenge 474: The Taxi Ride

What is the fastest way to get to KCLMS?

Eight mathematicians have booked a taxi to take them to KCLMS for a mathematics competition.

Unfortunately, when the taxi arrives, it can only carry four passengers instead of the requested eight.

KCLMS is 3 miles away. The mathematicians can all walk at 3 miles per hour, and the taxi can travel at 30 miles per hour.

The taxi driver suggests taking four mathematicians to KCLMS while the other four start to walk. When the taxi arrives at KCLMS, it will turn around, collect the remaining four mathematicians wherever they have reached, and then drive them to KCLMS.

(a) How long will this plan take?

The mathematicians have a better plan: the taxi should drop the first group off a little before they reach KCLMS and let them finish the journey on foot, then drive back to collect the remaining group of four wherever they have reached.

(b) What is the fastest they can reach KCLMS with this plan?

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.