Hannah and Jenna are travelling to a volleyball tournament in Grande Prairie, and leave at the same time. Hannah's parents drive her from Edmonton to grande Prairie, a distance of 460 km. Jenna's team takes a bus from Dawson Creek, BC to Grande Prairie, a distance of 130 km. Hannah's parents vehicle travels 10km/h faster than Jenna's, and Jenna arrives at the tournament 3 hours eairlier than Hannah. Determine how fast Hannah's parents are driving?
6 years ago
Answered By Jonny C
With questions like these, it might be best to divide up the information so you can better visualize what's going on:
Hannah
Distance = 460 km
Speed = Js+10km/h
Time = Jt+3h
We assign the variable "Js" for Jenna's speed because we don't know Jenna's speed. But we do know Hannah is traveling 10km/h faster so Hannah's speed would be Js+10km/h
We give the variable "Jt" to Jenna for time because we don't know the time it took Jenna to arrive. But we do know Hannah arrives 3 hours later so that would mean Hannah's time is Jt+3.
Jenna
Distance = 130 km
Speed = Js
Time = J
We also know that speed = distance/time
Therefore Hannah's speed formula would be (Js+10) = 460/(Jt+3)
and Jenna's speed formula would be Js = 130/Jt
At this point you have two formulas and two variables. You can use the substitution method to replace one of the variables. But before you do this I would advise that you expand Hannah's formula so that all variables are on one side of the equation.
(Js+10)(Jt+3) = 460
FOIL
JsJt + 3Js + 10Jt + 30 = 460
Because Js = 130/Jt (that's Jenna's formula) you can subtitute 130/Jt for Js in the expanded formula for Hannah.
Jt(130/Jt) + 3(130/Jt) +10Jt + 30 = 460
Simplify
130 + 390/Jt + 10Jt + 30 = 460
Combine the integers
390/Jt + 10Jt = 300
Now you have to multiply the entire equation by Jt to get rid of the fraction.
390 + 10Jt2 = 300Jt
The entire equation can be divided by 10
39 + 10Jt2 = 30Jt
Now you have a quadratic formula, so move everything to one side to make it equal to zero and solve its roots.
10Jt2 - 30Jt +39 = 0
Since this equation cannot be factored you have to use the quadratic formula.
Jt = 30 +/- sqrt[(-30)2 - 4(10)(39)] / 2(10)
Jt = 28.6 and 1.36
Because it would be unreasonable to believe it took Jenna 28.6 hours to travel 130km (because no one drives that slow) we can disregard the first answer and claim that it took Jenna 1.36h to arrive to Grande Prairie.
Js = 130/1.36
Js = 95.6km/h
If Hannah's parents were driving 10km/h faster than Jenna's bus, then Hannah's parents would be driving at 105.6km/h.
We can varify this answer by checking how long it would take Hannah to arrive.
Time = 460/105.6
Time for Hannah to arrive = 4.36 hours which is exactly 3 hours from Jenna's time. So the answer is 105.6km/h.
6 years ago
Answered By Jonny C
Sorry, a minor error, once you divide the entire equation by 10, you get Jt2 - 30Jt +39 = 0, I did this separately on paper so the answer is still the same.