Anuel traveled 4 hours nonstop to mexico, a total of 204 miles. he took a train part of the way, which averaged 60mph, and then took a bus the remaining distance, which averaged 40mph. how long was manuel on the train?

Let x be the total number of hours spent on the train

Let y be the total number of hours spent on the bus

Total hours spent on train and bus = x + y

Given that he travelled 4 hours

⇒ x + y = 4

Distance travelled = Time x Speed

Distance travelled on train = 60x miles

Distance travelled on Bus = 40y miles

Given that he travelled 204 miles

⇒ 60x + 40y = 204

The 2 equations formed are:

x + y = 4 ( 1 )

60x + 40y = 204 ( 2 )

Solve for x and y:

From (1) :

x + y = 4

⇒ x = 4 - y Sub into (2)

60 (4 - y) + 40y = 204

240 - 60y + 40y = 204

240 - 20y = 204

20y = 240 - 204

20y = 36

y = 1.8

x = 4 - y

x = 4 - 1.8

x = 2.2

Total time travelled on the train = x = 2.2 hours

Total time travelled on the bus = y = 1.8 hours

He was on the train for 2.2 hours