A superhero and his sidekick leave the city at the same time, flying towards a secret hideout 1800 km away. The superhero's speed is 100 km/h slower than the sidekick's, and he arrives 36 minutes later. What are their speeds?

Mathematics Questions

A superhero and his sidekick leave the city at the same time, flying towards a secret hideout 1800 km away. The superhero’s speed is 100 km/h slower than the sidekick’s, and he arrives 36 minutes later. What are their speeds?

Short Answer

The superhero’s speed is determined to be 500 km/h, while the sidekick’s speed is 600 km/h. The calculations were based on the time difference in their arrival and the relationship of their speeds.

Step-by-Step Solution

Step 1: Establish Variables and Given Information

First, define the speeds of the superhero and the sidekick. Let v represent the speed of the superhero. Given parameters include:

Superhero’s speed = v
Speed of the sidekick = v + 100 km/h
The time difference in arrival is 36 minutes, which is 0.6 hours

Step 2: Set Up the Equation

Next, construct an equation based on the distances traveled by both characters. The distance traveled is the same for both, so you can use the formula:

Distance = Speed ‚àöo Time
For the superhero: v ‚àöo (t + 0.6)
For the sidekick: (v + 100) ‚àöo t

Step 3: Solve the Equation

Finally, solve the derived equation. Substitute and rearrange to form a quadratic equation:

The resulting equation becomes 0.006v¬¨‚â§ + 0.6v – 1800 = 0.
Factoring gives (v – 500)(v + 600) = 0.
This leads to two possible speeds: v = 500 (superhero) and v = -600 (not valid).

Thus, the final speeds are 500 km/h for the superhero and 600 km/h for the sidekick.

A superhero and his sidekick leave the city at the …