406 algebra De mystif ieD
- Let t represent the number of hours Gary needs to unload the truck by
himself. John needs 36 minutes more than Gary needs to unload the
truck by himself, so John needs^3660 more hours or^35 more hours. The
number of hours John needs to unload the truck by himself is t +^35.
Together they can unload the truck in 1 hour 20 minutes, which is
113 = ^43 hours. This means that the Together rate is^114
3
4 1
3= ÷⋅= 3
43
4 .= Worker Quantity Rate TimeJohn (^113)
t+ 5
(^) t +^3
5
Gary^11 t t
Together 1 3
4
4
3
(^)
The equation to solve is^113
tt+^354
+ = . The LCD is^4 tt() + 53.
113
4
4 3
5
1 4 3
5
(^14)
(^35)
(^35)
tt
tt
t
tt
t
- +=
+
⋅
++
⋅=ttt
tt tt
tt
+
⋅
++
=+
3
5
3
4
443
5
3 3
5
44 ++=+
+=+
=+
12
5
3 9
5
8 12
5
3 9
5
58 12
5
53 9
2
2
2
tt
ttt
tt
55
40 12 15 9
0153112
0512 3
2
2
t
ttt
tt
t
+= +
=−−
=−()( tt+1)