Work out the speed in miles per hour at which colin drives home

  20 miles per hour

Step-by-step explanation:

The graph shows it takes Colin 45 minutes (3/4 hour) to drive home. For a given distance (the distance from home to market), the speed is inversely proportional to the time.

The time driving home is (3/4 hour)/(2/4 hour) = 3/2 times the time driving to the market. The inverse of this is 2/3, so Colin's speed driving home is ...

  (2/3)(30 mph) = 20 mph

The speed at which Colin drives home is 20 miles per hour.

Alternate solution

The distance to the market is ...

  distance = speed × time

  distance = (30 mi/h)(1/2 h) = 15 mi

The speed going home is ...

  speed = distance/time

  speed = (15 mi)/(3/4 h) = (15)(4/3) mi/h = 20 mi/h

x is variable or an unknown value to find

example:

2x = 5 which means x = 3