A student walks from his house at 2½ km/h and reaches his school late by 6 min. Next day, he increases his speed by 1.2 km/h and reaches 6 min before school time. How far is the school from his house?

1.5 km

Let the student take ‘x’ hours to reach at his normal speed.

When the student walks at 2.5 km/hr,

He reaches in (x + 6/60) hours

∴ Distance = 2.5 × (x + 0.1)      ----(1)

When the student walks at 3.7 km/hr,

He reaches in (x - 6/60) hours

∴ Distance = 3.7 × (x - 0.1)      ----(2)

From (1) and (2) we get,

∴ 2.5 (x + 0.1) = 3.7(x - 0.1)

∴ 2.5x + 0.25 = 3.7x - 0.37

∴ x = 0.517 hours

∴ From (1) we get

⇒ Distance = 2.5 × (0.517 + 0.1) ≈ 1.5 km