Jake rides his bike for the first 2/3 of the distance from home to sch

Solution

• Jake rides his bike for the first \(\frac{2}{3}\) of the distance from home to school at 10 mph
• He walks the remaining \(\frac{1}{3}\) distance at 3 mph
• Total travel time is 40 minutes or \(\frac{2}{3}\) hours

• The distance between Jake’s home to his school

• Distance travelled in bike = \(\frac{2x}{3}\) miles
• Therefore, time for bike travel = (\(\frac{2x}{3}\)/10) hours = \(\frac{x}{15}\) hours
• Distance travelled in walk = \(\frac{x}{3}\) miles
• Therefore, time for walk = (\(\frac{x}{3}\)/3) hours = \(\frac{x}{9}\) hours

• \(\frac{x}{15} + \frac{x}{9}\) = \(\frac{2}{3}\)
Or, \(\frac{8x}{45}\) = \(\frac{2}{3}\)
Or, x = \(\frac{90}{24}\) = \(\frac{15}{4}\) miles