Help With an Algebra Question?

Question

When Batman Began his pursuit, The Joker was already 60 miles ahead. if The Joker travels at 40 mph and Batman travels at 60 mph, how many hours will it take Batman to catch up with The Joker?

Answer 1

Batman and joker both travels in same direction 

Batman's given speed is 60 mph

Joker's given speed 40 mph

Batman travels faster than joker by  (60-40) 20 mph

Let's assume in x hours after starting Batman catches Joker

Hence in x hours Joker travels 40x miles and Batman travels 60x miles

when batman catches joker, Batman need to cover the initial distance of 60 miles between them, therefore: 60x=40x+60

=>60x-40x=60 ....... subtracting 40x from both sides

=>20x=60 ............... adjusting coefficients and operators

=>x=3 .................. dividing both sides by 20

 

Hence, Batman takes 3 hours to catch the Joker.

 

 

Answer 2

Hi Zach,

 

Here is the equation for Batman: 60t

Here is the equation for Joker: 60 + 40t

 

Set them to equal

 

60 + 40t  =  60t

 

60 = 20t     t = 3hrs

 

Extra info: both will reach 180 miles mark after 3hrs.

 

Let's check it:

 

Batman: 60 x 3 = 180     Joker: 60 + 40 x 3 = 60 + 120 = 180

 

It works.

 

Good luck to you.

Answer 3

Since Batman is going faster than the Joker, he is catching up to him, which lessens the gap between them.

 

Batman is going 60 mph, and the Joker 40 mph, so every hour, Batman gains 20 miles on the Joker.

 

The Joker started 60 miles ahead, so it will take 60/20 = 3 hours for Batman to make up that ground.