Yes. Whatever factor multiplies the speed, its inverse multiplies the time.
Walking → bicycle: speed 5 → 15, that is × 3
Time 18 → 6, that is ÷ 3
The speed grew 3 times; the time shrank to one-third.
Why it happens: The journey from Lucknow to Kanpur is the same 90 km whichever way you travel. Since speed × time must keep giving 90, tripling one factor forces the other to become a third of itself — nothing else can leave the product unchanged.
Q2.
Check if this is the case for the other modes of transport.
Answer
It holds for every pair in the table.
Change
Speed (km/h)
Time (hours)
Factors
Bicycle → motorcycle
15 → 30
6 → 3
× 2 and ÷ 2
Motorcycle → car
30 → 60
3 → 1.5
× 2 and ÷ 2
Walk → car
5 → 60
18 → 1.5
× 12 and ÷ 12
Bicycle → car
15 → 60
6 → 1.5
× 4 and ÷ 4
And the product is the same every time:
5 × 18 = 90 15 × 6 = 90 30 × 3 = 90 60 × 1.5 = 90
So xy = 90, where the constant k is the distance from Lucknow to Kanpur.
Why it happens: The book states the test as x₁/x₂ = y₂/y₁ — notice how the subscripts swap sides. For walking and the car: 5/60 = 0.08333… and 1.5/18 = 0.08333… too. That swap is the algebraic signature of an inverse proportion, and it comes straight from x₁y₁ = x₂y₂.