Question

Dr Hatton is running late for work. The hospital where he works is on the other side of a hill. He has four ways to get there. He can jog over the hill (5km) at 6.5 km/hr, or ride his bike along the 8km bike path at an average speed of 9.5km/hr. Alternatively he can drive his car along the windy, narrow road (22.5km) at an average speed of 30km/hr. His final option is to take an 8km journey on the cable car which travels at 12km/hr, however he needs to factor in that it will take him 7 minutes to purchase his ticket and get into one of the cabins to commence the journey.

Answer 1

Given :

There are 4 different paths to the hospital, one for jogging over a hill (5 km), one for bike riding (8 km), one for riding a car (22.5 km) and the last, through a cable car (8 km).

To Find :

Dr. Hatton is running late for his work, which is the best option.

Explanation :

Dr. Hatton is running late for his work at the hospital and he has four ways by which he can g there.

We will find the time taken by each way.

(a) The distance over the hill = 5 km

The speed at which he can jog over the hill = 6.5 km/hour

therefore time taken to reach the hospital by jogging  =  $\frac{5}{6.5}$

                                                                           =  0.76923 hours

Converting hours into minutes = 0.76923 × 60

                                                           = 46.15 ≈ 46 minutes

(b) Distance of hospital by bike path = 8 km

The average speed of bike = 9.5 km/hour

therefore time taken to reach hospital by bike riding = $\frac{8}{9.5}$

                                                           = 0.84210 hours

converting hours to minutes = 0.84210 × 60

                                               = 50.52 ≈ 50 minutes

(c) Distance of hospital by car path = 22.5 km

The average speed of the car = 30 km/hour

therefore time taken to reach hospital by car driving = $\frac{22.5}{30}$

                                                          = 0.75 hours

converting hours to minutes = 0.75 × 60

                                               = 45 minutes

(d) Distance of hospital by cable car = 8 km

The average speed of cable car = 12 km/hour

therefore time taken to reach hospital by cable car = $\frac{8}{12}$

                                                        = 0.67 hours

converting hours to minutes = 0.67 × 60 = 40 minutes

it will take him 7 minutes to purchase his tickets and get into one of the cabins

Therefore total time taken through a cable car= 7 + 40 = 47 minutes

Therefore, the minimum time consumption to reach hospital is 45 minutes, that is by driving car to work.