Math word problem Help!

Question

Trent and Dave drove 2420 km from Vancouver to Northern California. Trent drove 6 hours and Dave drove 12 hours. If Dave drove 5km/h faster than Trent at which speed did Dave drive at (to the nearest kilometer) ?

Answer 1

2420=r*6+(r+5)*12

2420=6r+12r+60

2420=18r+60

2420-60=18r

2360=18r

2360/18=r

131.111 km/hr=r is Trent's speed

131.111+5=136.111 km/hr is Dave's speed

Answer 2

We have that Dave and Trent each drove a portion of the total distance, let's call that TotalKM and can be written in equation form as:

(eq 1) TotalKM = DaveKM + TrentKM,

where DaveKM is the distance Dave drove and TrentKM is the distance Trent drove.

Distance can be calculated from speed multiplied by time driven, giving us 2 more equations:
(eq 2) DaveKM = DaveSpeed * 12 hours
(eq 3) TrentKM = TrentSpeed * 6 hours

Where DaveSpeed represents Dave's speed in km/hr and TrentSpeed represents Trent's speed in km/hr.

We are given that Dave drove at a speed 5km/hr faster than Trent and we can relate these speeds in equation form as:
(eq 4) DaveSpeed = TrentSpeed + 5 (all in km/hr)

Substituting (eq 4) into (eq 2) gives us the distance Dave traveled in terms of Trent's speed

(eq 5) DaveKM = (TrentSpeed + 5) * 12

We now have the distances that Dave and Trent each drove in equations 3 and 5, which we can substitute in to equation 1:

TotalKM = (TrentSpeed + 5) * 12 + TrentSpeed * 6.

We know from the information given that the total distance driven was 2420km, so this final equation becomes:

2420 = (TrentSpeed + 5) * 12 + TrentSpeed * 6

which is a single equation in terms of a single variable (TrentSpeed) which we can simplify using the following steps.

Multiply the right hand side terms:

2420 = 12*TrentSpeed + 60 + 6*TrentSpeed

Combine the common terms on right hand side:

2420 = (12+6)*TrentSpeed + 60

Subtract '60' from both sides:

2360 = 18*TrentSpeed

Divide both sides by '18':

131.11 = TrentSpeed

which gives us Trent's speed.  From (eq 4) Dave's speed is 5km/hr faster or:

DaveSpeed = 131.11 + 5 = 136.11

Rounding to nearest kilometer per hour we have DaveSpeed = 136 km/hr

 

 

 

Answer 3

Lets label some of the unknown things we are looking for, so we can write some equations that use the given information:

 

Suppose D = "the distance dave drove" and T = "the distance Trent drove", both in KMs

 

Then we have D/12 = dave's speed in KM/hr and T/6 = trent's speed in KM/hr

 

We know that Dave drove 5km/hr faster, so:

 

D/12 = T/6 + 5

 

We also know the total distance driven to be 2420 = T+D

 

We can substitute T =2420-D into the equation that relates speed and solve for D:

 

D/12 = (2420-D)/6 +5

 

Solving for D will yield the distance Dave drove, and dividing that by 12 will find Dave's speed in KM/hr.

 

D/12 + D/6 = 2420/6 +5

 

3D/12 = 2450/6

 

D = 4900/3 = 1633.333333...

 

Rounding to the nearest KM, Dave drove 1633 KMs in the 12hours he was behind the wheel

 

Thus Daves (average) speed is 1633/12 KM/hr or simply 136.1111...KM/hr

 

Hope that helps!