# Word problem

Doomtown is 200 miles due west of Sagebrush , and Joshua is due west of Doomtown. At 9am Mr Archer leaves Sagebrush for Joshua. At 1 pm. Mr Sassoon leaves Doomtown for Joshua. If Mr. Sassoon travels at an average speed 20 mph faster than Mr. Archer and they each reach Joshua at 4 pm how fast is each traveling?

Average Rating     Jun 11, 2010 Rating     Word Problem by: Karin This problem is dealing with distance, time and rate; therefore, we will be using the distance formula. D = rt. Let's first think of all the information that we know and don't know. Mr. Sassoon: Distance = D (We don't know the distance between Doomtown and Joshua) Rate = r + 20 (he travels 20mph faster than Mr. Archer) time = 3 hours (1:00pm - 4:00 pm) Mr. Archer: Time: 7 hours (travels from 9am - 4pm) Rate: r (we don't know his rate) Distance: D + 200 We labeled d as the distance between Doomstown and Joshua and we know that Sagebrush is 200 more miles from Doomtown. So, we now know that we have 2 unknown variables: r and d. Let's use the distance formula to write 2 equations; 1 for Mr. Sassoon, and 1 for Mr. Archer. Mr. Sassoon: d= rt d = (r+20)3 d = 3r + 60 (Distribute the 3) Mr. Archer: d = rt d+200 = r7 d + 200 = 7r (written properly) Now we can use our knowledge of solving a system of equations word problem. Using the substitution method is best because we know what d is equal to. So, let's substitute 3r + 60 into the equation: d + 200 = 7r 3r + 60 + 200 = 7r 3r + 260 = 7r Now let's solve for r. 3r + 260 = 7r 3r - 3r + 260 = 7r - 3r 260 = 4r 260/4 = 4r/4 65 = r Since r = 65, we know that Mr. Archer travels 65 mph and Mr.Sassoon travels 85 mph. (r+20) I hope this helps! Karin Need More Help With Your Algebra Studies?