Question

Karen drives straight south on Interstate 405 from the Santa Monica Freeway interchange going 10 miles per hour faster than Melinda, who leaves the same interchange at the same time going straight east on Interstate 10. After one hour they are 108 miles apart, measured by a straight line drawn between them. How fast is each driver going

Answer 1

Karen is moving at 81.2 miles per hour while Melinda is moving at 71.2 miles per hour.

Equation for speed

Speed is the ratio of total distance travelled to total time taken. It is given by:

Speed = distance / time

Let a represent Karen speed and b represent Melinda speed, hence:

a = b + 10

a - b = 10   (1)

Also:

a = d₁ / 1

d₁ = a

b = d₂/ 1 hour

d₂ = b

Since they are 108 miles apart, using Pythagoras:

108² = d₁² + d₂²

a² + b² = 11664

(b + 10)² + b² = 11664

b = 71.2 mph, a = 81.2 mph

Karen is moving at 81.2 miles per hour while Melinda is moving at 71.2 miles per hour.

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