Answer:
20 m/h
Step-by-step explanation:
You want the speed of a snail if the time it takes to travel 52 m is 1 hour and 36 minutes longer than the time it takes a turtle traveling 32 m/h faster.
The relation between time, speed, and distance is ...
time = distance/speed
If s represents the speed of the snail, then s+32 is the speed of the turtle. The relation between their times is ...
[tex]\dfrac{52}{s}=\dfrac{52}{s+32}+1.6[/tex]
where 1.6 hours is 1 hour 36 minutes.
Multiplying the equation by s(s+32), we have ...
52(s +32) = 52s +1.6s(s +32)
52s +1664 = 52s +1.6s² +51.2s . . . . . eliminate parentheses
1.6s² +51.2s -1664 = 0 . . . . . . . . . . put in standard form
s² +32s -1040 = 0 . . . . . . . . . . . divide by 1.6
This quadratic can be solved in any number of ways.
(s +32s +256) -1040 -256 = 0 . . . . . complete the square
(s +16)² = 1296 . . . . . . . . . . . . . . add 1296
s +16 = 36 . . . . . . . . . . . . . . positive square root
s = 20 . . . . . . . . . . . . . . subtract 16
The speed of the snail is 20 m/h.
