Final answer:
To reach home 7 minutes earlier than usual, Alex must increase his cycling speed to 13.2 kph. The closest given option is 14 kph (Option B).
Step-by-step explanation:
To calculate the new speed Alex needs to achieve to get home an additional 2 minutes earlier, we first need to determine the distance of his bike ride. We know his usual speed and time:
- Original speed: 9 kph (which is equivalent to 9 km/60 min = 0.15 km/min)
- Original time: 22 minutes
Using the formula distance = speed × time, we find Alex's usual route distance:
- Distance = 0.15 km/min × 22 min = 3.3 km
The new route takes 5 minutes less, so the time taken is 17 minutes. Alex wants to reduce this by a further 2 minutes, so he wants to complete the trip in 15 minutes. We reapply the distance = speed × time formula, rearranging it to solve for the new speed and using the original distance:
- New time = 17 min - 2 min = 15 minutes
- New speed = Distance / New time = 3.3 km / 15 min = 3.3 km / (15/60) h = 3.3 km / 0.25 h = 13.2 kph
Thus, Alex must cycle at 13.2 kph to reach home in the desired time. The closest option is Option B: 14 kph.