## Puzzling taxi fares

Concepts | Money, proportion |
---|---|

KS3 curriculum | 3.1c |

KS4 curriculum | 3.1c |

### Resources

### Teaching notes

The best way to introduce this is to ask students what is fair when sharing a taxi. The fundamental principle that they should arrive at is that the fare should be shared equally when there is multiple occupancy of the taxi, but any distance when there is sole occupancy should be the sole occupant’s responsibility.

For the purposes of this puzzle, one has to assume that the fare is proportional to the distance travelled, ie there is no set hire charge added on at the beginning of the journey.

### Solution

Based on the principle outlined above, for the first 10 km A and B share the £10 fare, paying £5 each. Then B continues on the journey and pays the remaining £10 himself. In total, *A pays £5* (a quarter of the total) and *B pays £15* (three quarters of the total).

### Extension

- Will the situation change if the two salesmen take a return journey rather than a single one?
- What if the taxi has a set hire charge (see above)?