Question

Alexandria wants to go hiking on Saturday. She will consider these conditions when she chooses which of several parks to visit: • She wants to hike for 2 hours. • She wants to spend no more than 6 hours away from home. • She can average 45 miles per hour to and from the park. Write and solve an inequality to find possible distances from Alexandria’s home to a park that satisfies the conditions.

Answer 1

120+45h ≤ 360

i converted the hours into minutes to make it easier

Answer 2

D = Distance to the park (round trip)

S = Average (driving) speed

T = Time (to get to the park)

HK = Hiking Time

OoH = Out of Home

D ≤ 0.5 * S/T

D ≤ 0.5 * S/(OoH - HK)

D ≤ 0.5 * 45/(6 - 2)

D ≤ 22.5/4

D ≤ 5.625 miles

Explanation:

T = Time (to get to the park)

HK = Hiking Time = 2 hours

OoH = Out of Home ≤ 6 hours

T = OoH - HK = 6-2 ≤ 4 hours

Now we know how much time does Alexandria have available for driving, Next, using the average speed, we can obtain possible distances:

S = Speed = 45 mph

D = Distance = 0.5 * S/T = 0.5 * 45/4 = 5.625 miles (or less)