While exploring for oil, it was necessary to carry at least 18 tonnes of supplies and 80 people into a desert region. Two types of vehicle were available: Landmasters and Sandrovers. Each Landmaster could carry 900 kg of supplies and 6 people. Each Sandrover could carry 1350kg of supplies and 5 people. If there were only 12 of each
type in good running order, what is the smallest number of vehicles necessary for the
journey?
To find the smallest number of vehicles necessary for the journey, we will consider each type of vehicle separately and calculate the total number of vehicles required for each.
Let's start with the Landmasters. Each Landmaster can carry 900 kg of supplies and 6 people. We need to transport at least 18 tonnes (18,000 kg) of supplies and 80 people. We can calculate the number of Landmasters required for supplies as follows:
Number of Landmasters required for supplies = Total supplies needed / Supplies capacity of each Landmaster
= 18,000 kg / 900 kg per Landmaster
= 20 Landmasters
Similarly, we can calculate the number of Landmasters required for people as follows:
Number of Landmasters required for people = Total people / People capacity of each Landmaster
= 80 people / 6 people per Landmaster
= 14 Landmasters
Therefore, we need at least 20 Landmasters for supplies and 14 Landmasters for people. But since we only have 12 Landmasters available, we will need to use all 12 of them for supplies and people.
Now let's do the same calculations for the Sandrovers. Each Sandrover can carry 1350 kg of supplies and 5 people. Using similar calculations as before, we find:
Number of Sandrovers required for supplies = Total supplies needed / Supplies capacity of each Sandrover
= 18,000 kg / 1350 kg per Sandrover
= 13.33 Sandrovers
Number of Sandrovers required for people = Total people / People capacity of each Sandrover
= 80 people / 5 people per Sandrover
= 16 Sandrovers
Therefore, we need at least 14 Sandrovers for supplies and 16 Sandrovers for people. Since we only have 12 Sandrovers available, we will need to use all 12 of them for supplies and people as well.
To calculate the total number of vehicles necessary for the journey, we add up the number of Landmasters and Sandrovers required for supplies and people:
Total number of Landmasters = Number of Landmasters for supplies + Number of Landmasters for people
= 20 + 14
= 34
Total number of Sandrovers = Number of Sandrovers for supplies + Number of Sandrovers for people
= 14 + 16
= 30
Therefore, the smallest number of vehicles necessary for the journey is 34 Landmasters and 30 Sandrovers, totaling 64 vehicles in total.