Pat's average driving speed is 25km/hr faster than Kelly's. In the same time Pat drives 356km and Kelly 256km.

Question

What is Pat's average driving speed?

Answer 1

if P is Pat's average speed, P-25 is Kelly's. distance is speed times time, or rather, time is distance divided by speed, and in this problem times are equal.

So Pat's time, 356/P, equals Kelly's time, 256/(P-25).

356/P = 256/(P-25).........cross multiply
356(P-25) = 256P
356P - 356•25 = 256P
356P - 256P = 356•25
100P = 8900
P = 89 km/h

Answer 2

Let x+25 = Pat's rate and x = Kelly's rate.
Pat's time to drive 356 km = 356 / (x+25).
Kelly's time to drive 256 km = 256 / x.
Since the two times are equal, the equation to solve is

356/(x+25) = 256/x
Cross multiply to get 356x=256(x+25)

356x - 256x = 6400
x=64 km/hr = Kelly's rate
x+25 = 89 = Pat's rate

Answer 3

Kelly speed: x kph (x km per hour)
Pat speed: (x+25) kph

t = time in hours

Pat distance: x * t = 256 km
Kelly distance: (x+25) * t = 356 km
---> x * t + 25 * t = 356 km

Substitute Pat distance into Kelly distance:
256 km + 25 * t = 356 km

Solve for t: t = 4 hours

Solve for x: x * 4 hours = 256 km

x = 64 kph (km/h)

Plug into Pat speed: 64 + 25 = 89 kph (km/h)

Answer 4

Let v(k) be Kelly velocity and v(p) be pats velocity. From the first statement, we know
V(p) = V(k) + 25.

From the second statement and knowing distance = velocity * time

Total Travel Time T = 356/V(p) = 256/V(k). From the
Now we have two equations with two unknowns.

using v(k) = v(p)-25 from the first equation. We know

256 * v(p) = 356 * v(k) 2nd equation

then
256 V(p) = 356(V(p) - 25) and solving
gives V(p) = 89 km/hr and Kellys is 64 Km/hr.

Answer 5

let Kelly's Speed=S
Then Pat's Speed=S+25
Distance=time*speed
Two equations:
Kellys Distance=256km=t(S)
Pat's Distance=356km=t(S+25)
Solving for S in the first equation:
S=256km/t
Substituting the answer into the second equation:
356km=t(256km/t+25)
multiply through by t
356km=256km+25t
subtracting like terms:
100km=25t
4=t
So they drive for 4 hours!
Kelly's average speed/hour=distance/time=256km/4h=64km per hour
64km/h+25km/h=89 km/h
to check we note that 356km/4=89km/h