Question 1156688
Let R[a], R[b], and R[c] = the rates of pumping
for the 3 pumps in gallons / hr
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(1) {{{ R[a] + R[b] + R[c] = 3700 }}}
(2) {{{ R[a] + R[b] = 2200 }}}
(3) {{{ R[a] + R[c] = 2400 }}}
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There are 3 equations and 3 unknowns, 
so it's solvable
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Subtract (2) from (1)
(1) {{{ R[a] + R[b] + R[c] = 3700 }}}
(2) {{{ -R[a] - R[b] = -2200 }}}
{{{ R[c] = 1500 }}}
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Subtract (3) from (1)
(1) {{{ R[a] + R[b] + R[c] = 3700 }}}
(3) {{{- R[a] - R[c] = -2400 }}}
{{{ R[b] = 1300 }}} 
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and
(3) {{{ R[a] + R[c] = 2400 }}}
(3) {{{ R[a] + 1500 = 2400 }}}
(3) {{{ R[a] = 900 }}}
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Pump A: 900 gal/hr
Pump B: 1300 gal/hr
Pump C: 1500 gal/hr
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check:
(1) {{{ R[a] + R[b] + R[c] = 3700 }}}
(1) {{{ 900 + 1300 + 1500 = 3700 }}}
(1) {{{ 3700 = 3700 }}}
OK