During a family trip, you share the driving with your dad. At most, you are allowed to drive for three
hours. While driving, your maximum speed is 55 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟.
a) Write a system of inequalities describing the possible numbers of hours 𝑡 and distance 𝑑 you
may have to drive.(4 marks)
b) Is it possible for you to have driven 170 𝑚𝑖𝑙𝑒𝑠?(1 mark

Question

During a family trip, you share the driving with your dad. At most, you are allowed to drive for three 
hours. While driving, your maximum speed is 55 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟.
a) Write a system of inequalities describing the possible numbers of hours 𝑡 and distance 𝑑 you 
may have to drive.(4 marks)
b) Is it possible for you to have driven 170 𝑚𝑖𝑙𝑒𝑠?(1 mark

Vocaloid · Answer

This is not a multiple choice question. It is asking for two separate calculations.

Part a) make one inequality for the hours. If t is hours and you’re allowed a maximum of 3 hours, then it stands to reason t must be less than or equal to 3. For the other inequality, make one for the distance driven. Distance = speed * time, so if t is less than or equal to 3, and the maximum speed is 55, what would be the maximum and minimum distances?

Part b) is 170 a possible solution for the distance inequality from part a)? If so, it’s possible to have driven 170 miles, and if not, it’s impossible to have driven that far.