finding speed of each bus

Question

An express bus travels a certain 320km route in 1 hour less time than it takes a local bus to travel a 300km route. Find the speed of each bus if the speed of the local is 20km/h less than that of the express.

Answer 1

Denote the express bus with label 1, and the local bus with label 2. The formula to use here is distance = speed X time.

 

Express bus:

d1 = 320 km

t - 1 hours is time

v1 = speed of express bus

 

Local bus

d2 = 300 km

t hours is time

v2 = v1 - 20 km/h is speed of local bus

 

Express bus:

d1 = 320 = v1(t - 1)

 

Local bus:

d2 = 300 = (v1 - 20)t

 

We have two equations and two unknowns, v1 and t. We want to find the speeds, so let us solve each equation for t and eliminate t.

 

t - 1 = 320/v1

t = 300/(v1 - 20)

 

 

t = 320/v1 + 1

t = 300/(v1 - 20)

 

Now set the two equations equal to each other to eliminate t.

 

320/v1 + 1 = 300/(v1 - 20)

 

(320 + v1)/v1 = 300/(v1 - 20)

 

Cross multiply.

 

(320 + v1)(v1 - 20) = 300v1

 

320v1 - 6400 + (v1)² - 20v1 = 300v1

 

(v1)² - 6400 = 0

 

(v1)² = 6400

 

v1 = 80 km/h  = speed of express bus

 

v1 - 20 = 60 km/h = speed of local bus