Question

Masha biked 20km 20 minutes faster than Dasha biked 20km. Find the speed of each cyclist if one biked 2km/h faster than the other.

Answer 1

• 12 km/h and 10 km/h

Explanation:

Let the speed of Masha = s, speed of Dasha = d

• Distance = 20 km
• Time difference = 20 min = 1/3 hr
• Speed difference = 2 km/h

As per above info we get following equations:

• s = d + 2
• 20/s + 1/3 = 20/d

Substitute s and solve for d:

• 20/(d + 2) + 1/3 = 20/d

Get rid of fraction by multiplying all terms by 3d(d + 2):

• 60d + d(d + 2) = 60(d + 2)
• 60d + d² + 2d = 60d + 120
• d² + 2d = 120
• d² + 2d + 1 = 121
• (d + 1)² = 11²
• d + 1 = 11
• d = 10

Find s:

• s = 10 + 2 = 12

The answer is

• Masha's speed 12 km/h and Dasha's speed 10 km/h