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A 30 km bicycle race is held on a straight road between two towns. The race has three segments:
1. The first 40% of the race is on a flat road.
2. The next 30% is uphill.
3. The remaining 30% is downhill.
Sarah cycles at an average speed of 20 km/h on flat roads, 10 km/h uphill, and 30 km/h downhill.
How long, in minutes, does it take Sarah to complete the entire race?
Let’s solve this problem step by step:
1. Calculate the distance of each segment:
– Flat road: 40% of 30 km = 0.4 × 30 = 12 km
– Uphill: 30% of 30 km = 0.3 × 30 = 9 km
– Downhill: 30% of 30 km = 0.3 × 30 = 9 km
2. Calculate the time taken for each segment:
– Flat road: Distance ÷ Speed = 12 km ÷ 20 km/h = 0.6 hours
– Uphill: Distance ÷ Speed = 9 km ÷ 10 km/h = 0.9 hours
– Downhill: Distance ÷ Speed = 9 km ÷ 30 km/h = 0.3 hours
3. Sum up the total time:
Total time = 0.6 + 0.9 + 0.3 = 1.8 hours
4. Convert hours to minutes:
1.8 hours = 1.8 × 60 minutes = 108 minutes
Therefore, it takes Sarah 108 minutes to complete the entire race.