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Let the distance be d km
time = speed/distance
The journey to the second town took: t1 = d km ÷ 2.5 km/h = d/2.5 hr = 2d/5 hr
The journey back to the first town took: t2 = d km ÷ 3 km/h = d/3 hr
The total time is: t1 + t2 = 7 hr 20 min = 7 + 20/60 hr = 7⅓ hr
→ 2d/5 + d/3 = 7⅓
→ (6d + 5d)/(3×5) = 7⅓
→ 11d = 7⅓ × 15
→ d = ((7×3+1)/3 × 15)/11
→ d = (22/3 × 15)/11
→ d = 22/11 × 15/3
→ d = 2 × 5 = 10
The towns are 10 km apart.
Checking:
t1 = 10 km ÷ 2.5 km/h = 4 hr
t2 = 10 km ÷ 3 km.h = 3⅓ hr
t = t1 + t2 = 4 hr + 3⅓ hr = 7⅓ hr
1 hr = 60 min
→ ⅓ hr = ⅓ × 60 min = 20 min
→ t = 7 hr 20 min.
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