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Algebra word problems

J is driving to Woods.  The graph representing his distance d from Woods in miles and the number of hours h he drives has a slope 50 and h-intercept 800.  What is J's average speed and how far from Woods was J at the start of the trip?


Consider describing the problem a little more or if you have the problem in front of you, copy it down word for word.  Maybe describe what the graph looks like if you are given the graph.  I have pored over this question and I am good with word problems and I can't make sense of what you wrote.  Make sure you are accurate with you writing because that is all we have to go off of.  

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2 Answers

Looks like a "trick problem" to me... I'll take a wild stab here... :-)   

If we make the vertical (y) axis be h (time in hours), and the horizontal (x) axis be d (distance in miles), then the h-intercept of 800 would be when d=0, presumably J's initial distance from Woods.  Therefore, J was 800 miles from Woods at the start of his/her trip.

If we consider that the slope is miles/hours, then 50mph would be J's average speed.


What you have is a Distance vs. Time graph, specifically Distance from Woods (miles) vs Time (hrs). The equation for the line is:

y = mx + b, where m = slope and b = intercept.

y = distance (d in miles)

x = time (t in hrs)

m = 50

b = 800

d = 50t + 800

The slope of the line is "rise over run"

- the rise is the change (Δ) in Distance from Woods (d) or Δd

- the run is the change (Δ) in Time(t) or Δt

The rise over run is Δd/Δt, which is speed. So he is going 50 miles/hr.

The start of his trip is at time = 0, so plug 0 into the equation for t:

d = 50t + 800

 = 50(0) + 800

 = 800 miles



Better answer than mine :-)