Question

Three jet-skis in a 300-kilometer handicap race leave at two-hour intervals. Jet-ski 1 leaves first and has an average speed of 25 kilometers per hour for the entire race. Jet-ski 2 leaves two hours later and has an average speed of 30 kilometers per hour for the entire race. Jet-ski 3 leaves last, two hours after jet-ski 2, and has an average speed of 40 kilometers per hour for the entire race.What is the algebraic explanation for the race outcome?

a) Jet-ski 1 wins due to the early start
b) Jet-ski 2 wins with a faster constant speed
c) Jet-ski 3 catches up and wins with the highest speed
d) Jet-ski 1 and Jet-ski 2 tie algebraically

Answer 1

After calculating the time it takes for each jet-ski to complete the 300-kilometer race given their respective speeds and starting times, it is determined that Jet-ski 3, which has the highest speed and starts last, catches up and finishes first, thus winning the race.

Step-by-step explanation:

To determine the algebraic outcome of the jet-ski race, we need to calculate the time it takes for each jet-ski to cover the 300-kilometer distance. Since time can be calculated by dividing the distance by the speed, we get the following formulas for each jet-ski:

• Time for Jet-ski 1 (T1) = Distance / Speed of Jet-ski 1 = 300 km / 25 km/h
• Time for Jet-ski 2 (T2) = (Time delay for Jet-ski 2 + Distance / Speed of Jet-ski 2) = 2 hours + (300 km / 30 km/h)
• Time for Jet-ski 3 (T3) = (Time delay for Jet-ski 3 + Distance / Speed of Jet-ski 3) = 4 hours + (300 km / 40 km/h)

Substituting the values into the formulas:

• T1 = 300 km / 25 km/h = 12 hours
• T2 = 2 hours + (300 km / 30 km/h) = 2 hours + 10 hours = 12 hours
• T3 = 4 hours + (300 km / 40 km/h) = 4 hours + 7.5 hours = 11.5 hours

Since Jet-ski 3 finishes the race in the least amount of time, Jet-ski 3 catches up and wins with the highest speed. Therefore, the correct answer to the algebraic explanation for the race outcome is (c) Jet-ski 3 catches up and wins with the highest speed.