Question

A superhero and his sidekick simultaneously leave the city and fly toward a secret hideout that is 1800 km away. The superhero's speed is 100 km/h slower than the sidekick's speed, and so he arrives at the hideout 36 minutes after his sidekick. Find the speed of each

Answer 1

Answer:

Speed of sidekick : 600

Speed of superhero : 500

Step-by-step explanation:

x = sidekick speed

speed of hero = x-100

Time of hero = -36

1800/(x-100) = (1800/x) + 0.6

That equations solves to x = 600 and x = 500 or -500

Answer 2

The given difference in speed and the arrival time, as well as the

distance traveled, gives the speeds as 500 and 600 km/hr.

Response:

• The speed of the superhero is 500 km/hr.

• The speed of the sidekick is 600 km/hr.

Which method is used to calculate the speed of the superhero, and the sidekick?

The given parameters are;

Superhero's speed = 1800 km

Speed of the superhero = Speed of the sidekick - 100 km/h

The time the superhero arrives at the hideout = 36 minutes after the sidekick = 0.6 hours

Required:

The speed of the superhero and the sidekick

Solution:

Let v represent the speed of the superhero, we have;

v × (t + 0.6) = (v + 100) × t

v·t + 0.6·v = v·t + 100·t = 1800

0.6·v = 100·t

$t = \dfrac{0.6}{100} \cdot v$

Therefore;

0.006·v² + 0.6·v - 1800 = 0

Which gives;

v² + 100·v - 300,000 = 0

(v - 500)·(v + 600) = 0

v = 500, or v = -600

• The speed of the superhero is 500 km/h

• The speed of the sidekick is 500 km/h + 100 km/h = 600 km/h

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