English | Español

The Problem

An elderly wildebeest scents a lion and stars running away at 40mph. .02hours later (about 1 minute) the lion starts running after the wildebeest at 50mph. Presuming the lion and the wildebeest started from the same spot, how long will it take the lion to catch the wildebeest? Use the 5step process, Also, be sure to draw a distance diagram and fill in a table to set up the problem. Use variables to represent your unknowns and draw a diagram, and draw a table, and set up and solve your equation.

Answer provided by our tutors

Given 

Speed of the wildbeast = 40 mph

Speed of the Lion = 50 mph

Time after which the Lion starts to chase = 0.02 hour

Variables

Time taken by the Lion to catch the wildbeast = t (hour)

Distance Travelled by the Lion during t hour = X 

Distance Travelled by the Wildbeast during t hour = Y

Solution 

Distance Travelled by the Wildbeast after 0.02 hour = 0.02 * 40 = 0.8 miles

Lion starts to run after 0.02 hour wildbeast so the total distance convered by Lion = Distance covered by wildbeast in t hour + 0.8 mile ( which it gained by starting 0.02 hour ahead of Lion)

Eqn 

X = Y + 0.8 ------- (1)

Speed = Distance travelled / time taken

Wildbeast

40 = Y / t

t = Y / 40 ----- (2)

Lion

50 = X / t

t = X / 50 ---- (3)

equating (2) and (3) as time taken t is same,

Y / 40  = X / 50

using equation (1) in the above equation

Y / 40 = (Y + 0.8) / 50 

Y * 50 = ( Y + 0.8) * 40

5Y = 4Y + 3.2

Y = 3.2 miles

X = 4 miles

using equation (2) 

Time taken t = 3.2 / 40

Time taken t = 0.08 hours = 4.8 minutes

Time taken for the Lion to catch the Wildbeast = 4.8 minutes or 0.08 hours

 

← Previous Problem Next Problem →