Dennis reads 39 pages in a hour. If Dennis begins to read at 1 pm and Ashley begins to read at 1:40 pm, at what time will they be reading the same exact page ?

Question

equation word problems

Answer 1

If Ashley reads more slowly than Dennis, then they will never read the same page at the same time. That said, let's go ahead and solve this assuming Ashley's rate is faster than Dennis's rate.

 

t = time elapsed in hours after 1 pm

 

Note that 40 min = 2/3 h

 

d = Dennis's rate = 39 pages/h

 

a = Ashley's rate = a pages/h

 

 

39t = a[t – (2/3)] = at – 2a/3

 

39t – at = –(2a)/3

 

t(39 – a) = –(2a)/3

 

t = [–(2a)/3]/(39 – a) = –(2a)/(117 – 3a) = time, in hours, in terms of a, after 1 pm.

 

 

UPDATE: With a = 52 pages/h, t = 2 h 40 min. Add this to 1 pm, and you have 3:40 pm.